Kamaleldin Abodayeh

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The asymptotic iteration method for the angular spheroidal eigenvalues

2005-01-27

T. Barakat , Kamaleldin Abodayeh , Aiman Mukheimer

The asymptotic iteration method is applied to calculate the angular spheroidal eigenvalues λmℓ(c). It is shown that this method asymptotically gives accurate results over the full range of parameter values, … The asymptotic iteration method is applied to calculate the angular spheroidal eigenvalues λmℓ(c). It is shown that this method asymptotically gives accurate results over the full range of parameter values, ℓ, m and c.

New Oscillation Criteria for Forced Nonlinear Fractional Difference Equations

2016-10-27

Bahaaeldin Abdalla , Kamaleldin Abodayeh , Thabet Abdeljawad +1 more

Predictor–Corrector Scheme for Electrical Magnetohydrodynamic (MHD) Casson Nanofluid Flow: A Computational Study

2023-01-16

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

The novelty of this paper is to propose a numerical method for solving ordinary differential equations of the first order that include both linear and nonlinear terms (ODEs). The method … The novelty of this paper is to propose a numerical method for solving ordinary differential equations of the first order that include both linear and nonlinear terms (ODEs). The method is constructed in two stages, which may be called predictor and corrector stages. The predictor stage uses the dependent variable’s first- and second-order derivative in the given differential equation. In literature, most predictor–corrector schemes utilize the first-order derivative of the dependent variable. The stability region of the method is found for linear scalar first-order ODEs. In addition, a mathematical model for boundary layer flow over the sheet is modified with electrical and magnetic effects. The model’s governing equations are expressed in partial differential equations (PDEs), and their corresponding dimensionless ODE form is solved with the proposed scheme. A shooting method is adopted to overcome the deficiency of the scheme for solving only first-order boundary value ODEs. An iterative approach is also considered because the proposed scheme combines explicit and implicit concepts. The method is also compared with an existing method, producing faster convergence than an existing one. The obtained results show that the velocity profile escalates by rising electric variables. The findings provided in this study can serve as a helpful guide for investigations into fluid flow in closed-off industrial settings in the future.

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Analytical study of transmission dynamics of 2019-nCoV pandemic via fractal fractional operator

2021-03-23

Mohammed A. ‬Almalahi , Satish K. Panchal , Wasfı Shatanawi +3 more

Through this paper, we aim to study the dynamics of 2019-nCoV transmission using fractal-ABC type fractional differential equations by incorporating population self-protection behavior changes. The basic parameters of disease dynamics … Through this paper, we aim to study the dynamics of 2019-nCoV transmission using fractal-ABC type fractional differential equations by incorporating population self-protection behavior changes. The basic parameters of disease dynamics spread differently from country to country due to the different sensitive parameters. The proposed model in this study links the infection rate, the marginal value of the infection force for the population, the recovery rate, the rate of decomposition of the 2019-nCoV in the environment, and what methods are needed to stop the spread of the virus. We give a detailed analysis of the proposed model in this study by analyzing disease-free equilibrium point, the number of reproduction and the positivity of the model solutions, in addition to verifying the existence, uniqueness and stability of this disease using fixed point theories. Further on exploiting Adam Bash's numerical scheme, we compute some numerical results for the required model. The concerned results have been simulated against some real initial data of three different counties including China, Brazil, and Italy.

Rectangular Metric-Like Type Spaces and Related Fixed Points

2018-09-03

Nabil Mlaiki , Kamaleldin Abodayeh , Hassen Aydi +2 more

In this paper, we introduce the concept of a rectangular metric-like space, along with its topology, and we prove some fixed point theorems for different contraction types. We also introduce … In this paper, we introduce the concept of a rectangular metric-like space, along with its topology, and we prove some fixed point theorems for different contraction types. We also introduce the concept of modified metric-like spaces and we prove some topological and convergence properties under the symmetric convergence. Some examples are given to illustrate the new introduced metric type spaces.

A Numerical Efficient Technique for the Solution of Susceptible Infected Recovered Epidemic Model

2020-01-01

Muhammad Shoaib Arif , Ali Raza , Kamaleldin Abodayeh +3 more

The essential features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. The … The essential features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. The aim of ... | Find, read and cite all the research you need on Tech Science Press

Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method

2006-06-01

T. Barakat , Kamaleldin Abodayeh , Omar M. Aldossary

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An explicit‐implicit numerical scheme for time fractional boundary layer flows

2022-03-10

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

Abstract This contribution is concerned with constructing a fractional explicit‐implicit numerical scheme for solving time‐dependent partial differential equations. The proposed scheme has the advantage over some existing explicit in providing … Abstract This contribution is concerned with constructing a fractional explicit‐implicit numerical scheme for solving time‐dependent partial differential equations. The proposed scheme has the advantage over some existing explicit in providing better stability region. But it has one of its limitations of being conditionally stable, even having one implicit stage. For spatial discretization, a fourth‐order compact scheme is considered. The stability and convergence of the proposed scheme for respectively the scalar parabolic equation and system of parabolic equations are given. For the sake of application of the scheme, fractional models of flow between parallel plates and mixed convection flow of Stokes' problems under the effects of viscous dissipation and thermal radiation are constructed. The proposed scheme for the classical model is also compared with built‐in Matlab solver pdepe for solving parabolic and elliptic equations and existing numerical schemes. It is found that Matlab solver pdepe is failed to find the solution of the considered flow problem with larger values of Eckert number or coefficient of the nonlinear term. But, the proposed scheme successfully finds the solution for classical and fractional models and shows faster convergence than the existing scheme. We provide illustrative computer simulations to show the principal computational features of this approach.

A Third-Order Two-Stage Numerical Scheme for Fractional Stokes Problems: A Comparative Computational Study

2022-06-14

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

Abstract A third-order numerical scheme is proposed for solving fractional partial differential equations (PDEs). The first explicit stage can converge fast, and the second implicit stage is responsible for enlarging … Abstract A third-order numerical scheme is proposed for solving fractional partial differential equations (PDEs). The first explicit stage can converge fast, and the second implicit stage is responsible for enlarging the stability region. The fourth-order compact scheme is employed to discretize spatial derivative terms. The stability of the scheme is given for the standard fractional parabolic equation, whereas convergence of the proposed scheme is given for the system of fractional parabolic equations. Mathematical models for heat and mass transfer of Stokes first and second problems using Dufour and Soret effects are given in a set of linear and nonlinear PDEs. Later on, these governing equations are converted into dimensionless PDEs. It is shown that the proposed scheme effectively solves the fractional forms of dimensionless models numerically, and a comparison is also conducted with existing schemes. If readers want it, a computational code for the discrete model system suggested in this paper may be made accessible to them for their convenience.

Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study

2023-05-27

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and … To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples in the literature do not provide third-order accuracy in two stages. The scheme was explicit and correct to the third order. The stability region and consistency analysis of the scheme for linear ODE are provided in this paper. Moreover, a mathematical model of heat and mass transfer for the non-Newtonian Casson nanofluid flow is given under the effects of the induced magnetic field, which was explored quantitatively using the method of Levenberg–Marquardt back propagation artificial neural networks. The governing equations were reduced to ODEs using suitable similarity transformations and later solved by the proposed scheme with a third-order accuracy. Additionally, a neural network approach for input and output/predicted values is given. In addition, inputs for velocity, temperature, and concentration profiles were mapped to the outputs using a neural network. The results are displayed in different types of graphs. Absolute error, regression studies, mean square error, and error histogram analyses are presented to validate the suggested neural networks’ performance. The neural network technique is currently used on three of these four targets. Two hundred points were utilized, with 140 samples used for training, 30 samples used for validation, and 30 samples used for testing. These findings demonstrate the efficacy of artificial neural networks in forecasting and optimizing complex systems.

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Hybrid Contractions on Branciari Type Distance Spaces

2019-10-19

Kamaleldin Abodayeh , Erdal Karapınar , Ariana Pitea +1 more

In this manuscript, we consider some hybrid contractions that merge linear and nonlinear contractions in the abstract spaces induced by the Branciari distance and the Branciari b-distance. More precisely, we … In this manuscript, we consider some hybrid contractions that merge linear and nonlinear contractions in the abstract spaces induced by the Branciari distance and the Branciari b-distance. More precisely, we introduce the notion of a ( p , c ) -weight type ψ -contraction in the setting of Branciari distance spaces and the concept of a ( p , c ) -weight type contraction in Branciari b-distance spaces. We investigate the existence of a fixed point of such operators in Branciari type distance spaces and illustrate some examples to show that the presented results are genuine in the literature.

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Existence and stability of nonlinear discrete fractional initial value problems with application to vibrating eardrum

2021-01-01

A‎. George Maria Selvam , Jehad Alzabut , D. Vignesh +2 more

<abstract> It is well known that Newton's second law can be applied in various biological processes including the behavior of vibrating eardrums. In this work, we consider a nonlinear discrete … <abstract> It is well known that Newton's second law can be applied in various biological processes including the behavior of vibrating eardrums. In this work, we consider a nonlinear discrete fractional initial value problem as a model describing the dynamic of vibrating eardrum. We establish sufficient conditions for the existence, uniqueness, and Hyers-Ulam stability for the solutions of the proposed model. To examine the validity of our findings, a concrete example of forced eardrum equation along with numerical simulation is analyzed. </abstract>

The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

2006-02-01

T. Barakat , Kamaleldin Abodayeh , B. Abdallah +1 more

The asymptotic iteration method is applied, to calculate the angular spheroidal eigenvalues $\lambda^{m}_{\ell}(c)$ with arbitrary complex size parameter $c$. It is shown that, the obtained numerical results of $\lambda^{m}_{\ell}(c)$ are … The asymptotic iteration method is applied, to calculate the angular spheroidal eigenvalues $\lambda^{m}_{\ell}(c)$ with arbitrary complex size parameter $c$. It is shown that, the obtained numerical results of $\lambda^{m}_{\ell}(c)$ are all in excellent agreement with the available published data over the full range of parameter values $\ell$, $m$, and $c$. Some representative values of $\lambda^{m}_{\ell}(c)$ for large real $c$ are also given.

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Numerical Schemes for Fractional Energy Balance Model of Climate Change with Diffusion Effects

2023-05-03

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

This study aims to propose numerical schemes for fractional time discretization of partial differential equations (PDEs). The scheme is comprised of two stages. Using von Neumann stability analysis, we ensure … This study aims to propose numerical schemes for fractional time discretization of partial differential equations (PDEs). The scheme is comprised of two stages. Using von Neumann stability analysis, we ensure the robustness of the scheme. The energy balance model for climate change is modified by adding source terms. The local stability analysis of the model is presented. Also, the fractional model in the form of PDEs with the effect of diffusion is given and solved by applying the proposed scheme. The proposed scheme is compared with the existing scheme, which shows a faster convergence of the presented scheme than the existing one. The effects of feedback, deep ocean heat uptake, and heat source parameters on global mean surface and deep ocean temperatures are displayed in graphs. The current study is cemented by the fact-based popular approximations of the surveys and modeling techniques, which have been the focus of several researchers for thousands of years.Mathematics Subject Classification:65P99, 86Axx, 35Fxx. Doi: 10.28991/ESJ-2023-07-03-011 Full Text: PDF

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New Exact Solutions of Landau-Ginzburg-Higgs Equation Using Power Index Method

2023-01-12

Khalil Ahmad , Khudija Bibi , Muhammad Shoaib Arif +1 more

In the present study, the optimality approach is applied to find the exact solution of the Landau-Ginzburg-Higgs Equation (LGHE) using new transformations. This method is a direct algebraic method for … In the present study, the optimality approach is applied to find the exact solution of the Landau-Ginzburg-Higgs Equation (LGHE) using new transformations. This method is a direct algebraic method for obtaining exact solutions of nonlinear differential equations. We find suitable solutions of the LGHE in terms of elliptic Jacobi functions by applying transformations of basic functions. Exact solutions of the equations are obtained with the help of symbolic software (Maple) which allows the computation of equations with parameter constants. It is exposed that PIM is influential, suitable, and shortest and offers an exact solution of LGHE.

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Relations Between partial Metric Spaces and M-Metric Spaces, Caristi Kirk's Theorem in $M-$Metric Type Spaces

2015-01-01

Kamaleldin Abodayeh , Nabil Mlaiki , Thabet Abdeljawad +1 more

Very recently, Mehadi et al [M. Asadi, E. Karap{\i}nar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on $M-$metric spaces] extended the partial metric spaces … Very recently, Mehadi et al [M. Asadi, E. Karap{\i}nar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on $M-$metric spaces] extended the partial metric spaces to the notion of $M-$metric spaces. In this article, we study some relations between partial metric spaces and $M-$metric spaces. Also, we generalize Caristi Kirki's Theorem from partial metric spaces to $M-$metric spaces, where we corrected some gaps in the proof of the main Theorem in E. Karap\i nar [E. Karap\i nar, Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011: 4, (2011)]. We close our contribution by introducing some examples to validate and verify our extension results.

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New theorems on extended b-metric spaces under new contractions

2019-11-07

Aiman Mukheimer , Nabil Mlaiki , Kamaleldin Abodayeh +1 more

The notion of extended b-metric space plays an important role in the field of applied analysis to construct new theorems in the field of fixed point theory. In this paper, … The notion of extended b-metric space plays an important role in the field of applied analysis to construct new theorems in the field of fixed point theory. In this paper, we construct and prove new theorems in the filed of fixed point theorems under some new contractions. Our results extend and modify many existing results in the literature. Also, we provide an example to show the validity of our results. Moreover, we apply our result to solve the existence and uniqueness of such equations.

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Nonlocal and multiple-point fractional boundary value problem in the frame of a generalized Hilfer derivative

2021-06-15

Wasfı Shatanawi , Abdelatif Boutiara , Mohammed S. ‬Abdo +2 more

Abstract The aim of this manuscript is to handle the nonlocal boundary value problem for a specific kind of nonlinear fractional differential equations involving a ξ -Hilfer derivative. The used … Abstract The aim of this manuscript is to handle the nonlocal boundary value problem for a specific kind of nonlinear fractional differential equations involving a ξ -Hilfer derivative. The used fractional operator is generated by the kernel of the kind $k(\vartheta,s)=\xi (\vartheta )-\xi (s)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mo>(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>ξ</mml:mi><mml:mo>(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo>)</mml:mo><mml:mo>−</mml:mo><mml:mi>ξ</mml:mi><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:math> and the operator of differentiation ${ D}_{\xi } = ( \frac{1}{\xi ^{\prime }(\vartheta )}\frac{d}{d\vartheta } ) $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>D</mml:mi><mml:mi>ξ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msup><mml:mi>ξ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>(</mml:mo><mml:mi>ϑ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac><mml:mfrac><mml:mi>d</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>ϑ</mml:mi></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:math> . The existence and uniqueness of solutions are established for the considered system. Our perspective relies on the properties of the generalized Hilfer derivative and the implementation of Krasnoselskii’s fixed point approach and Banach’s contraction principle with respect to the Bielecki norm to obtain the uniqueness of solution on a bounded domain in a Banach space. Besides, we discuss the Ulam–Hyers stability criteria for the main fractional system. Finally, some examples are given to illustrate the viability of the main theories.

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Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions

2021-11-03

Saleh S. Redhwan , Sadikali L. Shaikh , Mohammed S. ‬Abdo +4 more

<abstract>In this paper, we investigate a nonlinear generalized fractional differential equation with two-point and integral boundary conditions in the frame of $ \kappa $-Hilfer fractional derivative. The existence and uniqueness … <abstract>In this paper, we investigate a nonlinear generalized fractional differential equation with two-point and integral boundary conditions in the frame of $ \kappa $-Hilfer fractional derivative. The existence and uniqueness results are obtained using Krasnoselskii and Banach's fixed point theorems. We analyze different types of stability results of the proposed problem by using some mathematical methodologies. At the end of the paper, we present a numerical example to demonstrate and validate our findings.</abstract>

Generalized proportional fractional integral functional bounds in Minkowski’s inequalities

2021-09-17

Tariq A. Aljaaidi , Deepak B‎. ‎Pachpatte , Wasfı Shatanawi +2 more

Abstract In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ … Abstract In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ . The functions used in this work are bounded by two positive functions to get reverse Minkowski inequalities in a new sense. Moreover, we introduce new fractional integral inequalities which have a close relationship to the reverse Minkowski-type inequalities via ψ -proportional fractional integral, then with the help of this fractional integral operator, we discuss some new special cases of reverse Minkowski-type inequalities through this work. An open issue is covered in the conclusion section to extend the current findings to be more general.

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New Results in Controlled Metric Type Spaces

2021-04-01

Muhib Abuloha , Doaa Rizk , Kamaleldin Abodayeh +2 more

In this paper, a new class of functions denoted by <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow> <mi>ν</mi> </mrow> </msub> </math> is introduced which we use to prove new interesting … In this paper, a new class of functions denoted by <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mi mathvariant="normal">Ψ</mi> <mrow> <mi>ν</mi> </mrow> </msub> </math> is introduced which we use to prove new interesting fixed point results in controlled metric type spaces. Also, we present examples to illustrate our work.

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A Compact Numerical Scheme for the Heat Transfer of Mixed Convection Flow in Quantum Calculus

2022-05-13

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

This contribution aims to propose a compact numerical scheme to solve partial differential equations (PDEs) with q-spatial derivative terms. The numerical scheme is based on the q-Taylor series approach, and … This contribution aims to propose a compact numerical scheme to solve partial differential equations (PDEs) with q-spatial derivative terms. The numerical scheme is based on the q-Taylor series approach, and an operator is proposed, which is useful to discretize second-order spatial q-derivative terms. The compact numerical scheme is constructed using the proposed operator, which gives fourth-order accuracy for second-order q-derivative terms. For time discretization, Crank–Nicolson, and Runge–Kutta methods are applied. The stability for the scalar case and convergence conditions for the system of equations are provided. The mathematical model for the heat transfer of boundary layer flow under the effects of non-linear mixed convection is given in form of PDEs. The governing equations are transformed into dimensionless PDEs using suitable transformations. The velocity and temperature profiles with variations of mixed convection parameters and the Prandtl number are drawn graphically. From considered numerical experiments, it is pointed out that the proposed scheme in space and Crank–Nicolson in time is more effective than that in which discretization for the time derivative term is performed by applying the Runge–Kutta scheme. A comparison with existing schemes is carried out as part of the research. For future fluid-flow investigations in an enclosed industrial environment, the results presented in this study may serve as a useful guide.

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Potential-theoretic study of functions on an infinite network

2008-02-01

Kamaleldin Abodayeh , Victor Anandam

In the context of an infinite network $N$, the Dirichlet problem with respect to an arbitrary subset of vertices $N$ is solved.Using this solution, some of the important potential-theoretic concepts … In the context of an infinite network $N$, the Dirichlet problem with respect to an arbitrary subset of vertices $N$ is solved.Using this solution, some of the important potential-theoretic concepts like Balayage, Domination principle, and Poisson kernel are investigated in $N$.

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Fixed Point Results for Mapping of Nonlinear Contractive Conditions of $\alpha$ -Admissibility Form

2019-01-01

Wasfı Shatanawi , Kamaleldin Abodayeh

We introduce in this paper some concepts of α-admissible triangular mappings with respect to a function β and the concept of (α, β, ψ)-contraction. We also utilize our new concept … We introduce in this paper some concepts of α-admissible triangular mappings with respect to a function β and the concept of (α, β, ψ)-contraction. We also utilize our new concept to prove a fixed point theorem based on the contractive condition of type α-admissibility. We apply our main result to derive many fixed point results. Also, we construct some examples to support our work. In the literature, many exciting results are improved and extended using our results.

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A Computational Approach to a Mathematical Model of Climate Change Using Heat Sources and Diffusion

2022-07-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

The present work aims to extend the climate change energy balance models using a heat source. An ordinary differential equations (ODEs) model is extended to a partial differential equations (PDEs) … The present work aims to extend the climate change energy balance models using a heat source. An ordinary differential equations (ODEs) model is extended to a partial differential equations (PDEs) model using the effects of diffusion over the spatial variable. In addition, numerical schemes are presented using the Taylor series expansions. For the climate change model in the form of ODEs, a comparison of the presented scheme is made with the existing Trapezoidal method. It is found that the presented scheme converges faster than the existing scheme. Also, the proposed scheme provides fewer errors than the existing scheme. The PDEs model is also solved with the presented scheme, and the results are displayed in the form of different graphs. The impact of the climate feedback parameter, the heat uptake parameter of the deep ocean, and the heat source parameter on global mean surface temperature and deep ocean temperature is also portrayed. In addition, these recently developed techniques exhibit a high level of predictability. Doi: 10.28991/CEJ-2022-08-07-04 Full Text: PDF

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Contraction principles in M_s-metric spaces

2017-02-19

Nabil Mlaiki , Nizar Souayah , Kamaleldin Abodayeh +1 more

In this paper, we give an interesting extension of the partial S-metric space which was introduced [N.Mlaiki, Univers. In this paper, we give an interesting extension of the partial S-metric space which was introduced [N.Mlaiki, Univers.

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An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

2021-08-03

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +1 more

Abstract An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme … Abstract An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Furthermore, the scheme’s stability for the general type of parabolic equation with source term is proved by employing von Neumann stability analysis. Furthermore, the consistency of the scheme is verified for the category of susceptible individuals. In addition to this, the convergence of the proposed scheme is discussed for the considered mathematical model.

A Numerical Scheme for Fractional Mixed Convection Flow Over Flat and Oscillatory Plates

2022-05-03

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

Abstract A fractional scheme is proposed to solve time-fractional partial differential equations. According to the considered fractional Taylor series, the scheme is compact in space and provides fourth-order accuracy in … Abstract A fractional scheme is proposed to solve time-fractional partial differential equations. According to the considered fractional Taylor series, the scheme is compact in space and provides fourth-order accuracy in space and second-order accuracy in fractional time. The scheme is conditionally stable when applied to the scalar fractional parabolic equation. The convergence of the scheme is demonstrated for the system of fractional parabolic equations. Moreover, a fractional model for heat and mass transfer of mixed convection flow over the flat and oscillatory plate is given. The radiation effects and chemical reactions are also considered. The scheme is tested on this model and the nonlinear fractional Burgers equation. It is found that it is more accurate than considering existing schemes in most of the regions of the solution domain. The compact scheme with exact findings of spatial derivatives is better than considering linearized equations. The error obtained by the proposed scheme with the determination of exact spatial derivatives is better than that obtained by two explicit existing schemes. The main advantage of the proposed scheme is that it is capable of providing the solution for convection-diffusion equations with compact fourth-order accuracy. Still, the corresponding implicit compact scheme is unable to find the solution to convection-diffusion problems.

Stability Analysis of Fractional-Order Predator-Prey System with Consuming Food Resource

2023-01-07

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Asad Ejaz

The cardinal element of ecology is the predator-prey relationship. The population of interacting organisms is based on many factors such as food, water, space, and protection. A key component among … The cardinal element of ecology is the predator-prey relationship. The population of interacting organisms is based on many factors such as food, water, space, and protection. A key component among these factors is food. The presence of food for the organisms shapes the structure of the habitat. The present study considers a predator and two types of prey. It is assumed that one prey species utilizes the same food resource as the predator, whereas the other prey species depends on a different food resource. The existence and uniqueness of the model are studied using the Lipschitz condition. The fixed points for the fractional-order model are sorted out, and the existence of the equilibrium points is discussed. The stability analysis of the model for the biologically important fixed points is provided. These include the coexistence fixed point and the prey-free (using the same food resources as the predator does) fixed point. A fractional-order scheme is implemented to support theoretical results for the stability of equilibrium points. The time series solution of the model is presented in the form of plots. Moreover, the impact of some mathematically and biologically important parameters is presented.

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A two-stage multi-step numerical scheme for mixed convective Williamson nanofluid flow over flat and oscillatory sheets

2023-08-19

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +1 more

The novelty of this contribution is to propose an implicit numerical scheme for solving time-dependent boundary layer problems. The scheme is multi-step and consists of two stages. It is third-order … The novelty of this contribution is to propose an implicit numerical scheme for solving time-dependent boundary layer problems. The scheme is multi-step and consists of two stages. It is third-order accurate in time and constructed on three-time levels. For spatial discretization, a fourth-order compact scheme is adopted. The stability of the proposed scheme is analyzed for scalar linear partial differential equation (PDE) that shows its conditional stability. The convergence of the scheme is also provided for a system of time-dependent parabolic equations. Moreover, a mathematical model for heat and mass transfer of mixed convective Williamson nanofluid flow over flat and oscillatory sheets is modified with the characteristic of the Darcy–Forchheimer model. The results show that the temperature profile rises by developing thermophoresis and Brownian motion parameter values. Also, the proposed scheme is compared with an existing Crank–Nicolson method. It is found that the proposed scheme converges faster than the existing one for solving scalar linear PDE as well as the system of linear and nonlinear parabolic equations, which are dimensionless forms of governing equations of a flow phenomenon. The findings provided in this study can serve as a helpful guide for future investigations into fluid flow in closed-off industrial settings.

Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

2024-03-12

Esam Y. Salah , Bhausaheb Sontakke , Mohammed S. ‬Abdo +3 more

The mathematical model of the dynamics of HIV/AIDS infection transmission is developed by adding the set of infected but noninfectious persons, using a conformable fractional derivative in the Liouville–Caputo sense. … The mathematical model of the dynamics of HIV/AIDS infection transmission is developed by adding the set of infected but noninfectious persons, using a conformable fractional derivative in the Liouville–Caputo sense. Some fixed point theorems are applied to this model to investigate the existence and uniqueness of the solutions. It is determined what the system’s fundamental reproduction number <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math> is. The disease-free equilibrium displays the model’s stability and the local stability around the equilibrium. The study also examined the effects of different biological features on the system through numerical simulations using the Adams–Moulton approach. Additionally, varied values of fractional orders are simulated numerically, demonstrating that the results generated by the conformable fractional derivative-based model are more physiologically plausible than integer-order derivatives.

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Schrödinger networks and their Cartesian products

2020-11-16

Kamaleldin Abodayeh , Victor Anandam

A Schrödinger network is a suitable infinite graph on which certain potential‐theoretic aspects of the discrete Schrödinger equation can be studied. It is shown that the positive solutions of this … A Schrödinger network is a suitable infinite graph on which certain potential‐theoretic aspects of the discrete Schrödinger equation can be studied. It is shown that the positive solutions of this discrete equation can be represented as integrals. The Cartesian product of Schrödinger networks, which has a bearing on Markov chains, is investigated. Also, we give a characterization of minimal positive harmonic functions on the the Cartesian product of Schrödinger networks.

Oscillation theorems for higher order dynamic equations with superlinear neutral term

2021-01-01

Said R. Grace , Jehad Alzabut , Kamaleldin Abodayeh

<abstract> In this paper, several oscillation criteria for a class of higher order dynamic equations with superlinear neutral term are established. The proposed results provide a unified platform that adequately … <abstract> In this paper, several oscillation criteria for a class of higher order dynamic equations with superlinear neutral term are established. The proposed results provide a unified platform that adequately covers both discrete and continuous equations and further sufficiently comments on oscillatory behavior of more general class of equations than the ones reported in the literature. We conclude the paper by demonstrating illustrative examples. </abstract>

Dirichlet problem and Green's formulas on trees

2005-11-01

Kamaleldin Abodayeh , Victor Anandam

The Dirichlet problem and the construction of superharmonic functions with point harmonic singularities are two of the basic problems in potential theory. In this article, we study these problems in … The Dirichlet problem and the construction of superharmonic functions with point harmonic singularities are two of the basic problems in potential theory. In this article, we study these problems in the context of discrete potential theory, which leads to the consideration of Green's formulas and flux on a Cartier tree.

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Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces

2019-05-20

Wasfı Shatanawi , Kamaleldin Abodayeh

We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence … We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction.

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Stability Analysis of Predator-Prey System with Consuming Resource and Disease in Predator Species

2022-01-01

Asad Ejaz , Yasir Nawaz , Muhammad Shoaib Arif +2 more

The present study is concerned with formulating a predator-prey eco-epidemiological mathematical model assuming that an infection exists in the predator species. The two classes of predator species (susceptible and infected) … The present study is concerned with formulating a predator-prey eco-epidemiological mathematical model assuming that an infection exists in the predator species. The two classes of predator species (susceptible and infected) compete for the same sources available in the environment with the predation option. It is assumed that the disease does not spread vertically. The proposed model is analyzed for the stability of the coexistence of the predators and prey. The fixed points are carried out, and the coexisting fixed point is studied in detail by constructing the Lyapunov function. The movement of species in search of food or protection in their habitat has a significant influence, examined through diffusion. The ecological influences of self-diffusion on the population density of both species are studied. It is theoretically proved that all the under consideration species can coexist in the same environment. The coexistence fixed point is discussed for both diffusive and non-diffusive cases. Moreover, a numerical scheme is constructed for solving time-dependent partial differential equations. The stability of the scheme is given, and it is applied for solving presently modified eco-epidemiological mathematical model with and without diffusion. The comparison of the constructed scheme with two exiting schemes, Backward in Time and Central in Space (BTCS) and Crank Nicolson, is also given in the form of plots. Finally, we run a computer simulation to determine the effectiveness of the proposed numerical scheme. For readers’ convenience, a computational code for the proposed discrete model scheme may be made available upon request.

Computational Modeling of Reaction-Diffusion COVID-19 Model Having Isolated Compartment

2022-07-12

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Asad Ejaz

Cases of COVID-19 and its variant omicron are raised all across the world. The most lethal form and effect of COVID-19 are the omicron version, which has been reported in … Cases of COVID-19 and its variant omicron are raised all across the world. The most lethal form and effect of COVID-19 are the omicron version, which has been reported in tens of thousands of cases daily in numerous nations. Following WHO (World health organization) records on 30 December 2021, the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266, active, recovered, and discharge were found to be 82,402 and 34,258,778, respectively. While there were 160,989 active cases, 33,614,434 cured cases, 456,386 total deaths, and 605,885,769 total samples tested. So far, 1,438,322,742 individuals have been vaccinated. The coronavirus or COVID-19 is inciting panic for several reasons. It is a new virus that has affected the whole world. Scientists have introduced certain ways to prevent the virus. One can lower the danger of infection by reducing the contact rate with other persons. Avoiding crowded places and social events with many people reduces the chance of one being exposed to the virus. The deadly COVID-19 spreads speedily. It is thought that the upcoming waves of this pandemic will be even more dreadful. Mathematicians have presented several mathematical models to study the pandemic and predict future dangers. The need of the hour is to restrict the mobility to control the infection from spreading. Moreover, separating affected individuals from healthy people is essential to control the infection. We consider the COVID-19 model in which the population is divided into five compartments. The present model presents the population’s diffusion effects on all susceptible, exposed, infected, isolated, and recovered compartments. The reproductive number, which has a key role in the infectious models, is discussed. The equilibrium points and their stability is presented. For numerical simulations, finite difference (FD) schemes like nonstandard finite difference (NSFD), forward in time central in space (FTCS), and Crank Nicolson (CN) schemes are implemented. Some core characteristics of schemes like stability and consistency are calculated.

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Modelling Infectious Disease Dynamics: A Robust Computational Approach for Stochastic SIRS with Partial Immunity and an Incidence Rate

2023-11-27

Amani S. Baazeem , Yasir Nawaz , Muhammad Shoaib Arif +2 more

For decades, understanding the dynamics of infectious diseases and halting their spread has been a major focus of mathematical modelling and epidemiology. The stochastic SIRS (susceptible–infectious–recovered–susceptible) reaction–diffusion model is a … For decades, understanding the dynamics of infectious diseases and halting their spread has been a major focus of mathematical modelling and epidemiology. The stochastic SIRS (susceptible–infectious–recovered–susceptible) reaction–diffusion model is a complicated but crucial computational scheme due to the combination of partial immunity and an incidence rate. Considering the randomness of individual interactions and the spread of illnesses via space, this model is a powerful instrument for studying the spread and evolution of infectious diseases in populations with different immunity levels. A stochastic explicit finite difference scheme is proposed for solving stochastic partial differential equations. The scheme is comprised of predictor–corrector stages. The stability and consistency in the mean square sense are also provided. The scheme is applied to diffusive epidemic models with incidence rates and partial immunity. The proposed scheme with space’s second-order central difference formula solves deterministic and stochastic models. The effect of transmission rate and coefficient of partial immunity on susceptible, infected, and recovered people are also deliberated. The deterministic model is also solved by the existing Euler and non-standard finite difference methods, and it is found that the proposed scheme forms better than the existing non-standard finite difference method. Providing insights into disease dynamics, control tactics, and the influence of immunity, the computational framework for the stochastic SIRS reaction–diffusion model with partial immunity and an incidence rate has broad applications in epidemiology. Public health and disease control ultimately benefit from its application to the study and management of infectious illnesses in various settings.

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Remarks on Multiplicative Metric Spaces and Related Fixed Points

2015-01-01

Kamaleldin Abodayeh , Ariana Pitea , Wasfı Shatanawi +1 more

In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in … In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be obtained from the corresponding results in standard metric spaces.

Controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via Atangana-Baleanu Caputo fractional derivative

2024-03-26

Muhammad Sarwar , Sadam Hussain , Kamaleldin Abodayeh +2 more

This study mainly concerns the controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via the Atangana-Baleanu (AB) Caputo fractional derivative (FD). The essential findings are created using methods and … This study mainly concerns the controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via the Atangana-Baleanu (AB) Caputo fractional derivative (FD). The essential findings are created using methods and concepts from semigroup theory, stochastic theory, fractional calculus, K-set contraction, and measure of noncompactness. Finally, an example is provided to demonstrate the applications of the key findings.

Quasi-bounded supersolutions of discrete Schrodinger equations

2016-01-01

Kamaleldin Abodayeh , Victor Anandam

Solution of Some Impulsive Differential Equations via Coupled Fixed Point

2021-03-19

Ahmed Boudaoui , K. Mebarki , Wasfı Shatanawi +1 more

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system … In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

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Existence and Uniqueness Results of Coupled Fractional-Order Differential Systems Involving Riemann–Liouville Derivative in the Space Wa+γ1,1(a,b)×Wa+γ2,1(a,b) with Perov’s Fixed Point Theorem

2021-11-13

Noura Laksaci , Ahmed Boudaoui , Kamaleldin Abodayeh +2 more

This paper is devoted to studying the existence and uniqueness of a system of coupled fractional differential equations involving a Riemann–Liouville derivative in the Cartesian product of fractional Sobolev spaces … This paper is devoted to studying the existence and uniqueness of a system of coupled fractional differential equations involving a Riemann–Liouville derivative in the Cartesian product of fractional Sobolev spaces E=Wa+γ1,1(a,b)×Wa+γ2,1(a,b). Our strategy is to endow the space E with a vector-valued norm and apply the Perov fixed point theorem. An example is given to show the usefulness of our main results.

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Certain dynamic iterative scheme families and multi-valued fixed point results

2022-01-01

Amjad Ali , Muhammad Arshad , Eskandar Emeer +3 more

<abstract>The article presents a systematic investigation of an extension of the developments concerning $ F $-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of $ … <abstract>The article presents a systematic investigation of an extension of the developments concerning $ F $-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of $ F $-contractions to the case of non-linear ($ F $, $ F_{H} $)-dynamic-iterative scheme for Branciari Ćirić type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determined. The paper also includes a tangible example and a graphical interpretation that displays the motivation for such investigations. The work is illustrated by providing an application of the proposed non-linear ($ F $, $ F_{H} $)-dynamic-iterative scheme to the Liouville-Caputo fractional derivatives and fractional differential equations.</abstract>

Finite difference schemes for time-dependent convection q-diffusion problem

2022-01-01

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +1 more

<abstract>The energy balance ordinary differential equations (ODEs) model of climate change is extended to the partial differential equations (PDEs) model with convections and <italic>q</italic>-diffusions. Instead of integer order second-order partial … <abstract>The energy balance ordinary differential equations (ODEs) model of climate change is extended to the partial differential equations (PDEs) model with convections and <italic>q</italic>-diffusions. Instead of integer order second-order partial derivatives, partial <italic>q</italic>-derivatives are considered. The local stability analysis of the ODEs model is established using the Routh-Hurwitz criterion. A numerical scheme is constructed, which is explicit and second-order in time. For spatial derivatives, second-order central difference formulas are employed. The stability condition of the numerical scheme for the system of convection <italic>q</italic>-diffusion equations is found. Both types of ODEs and PDEs models are solved with the constructed scheme. A comparison of the constructed scheme with the existing first-order scheme is also made. The graphical results show that global mean surface and ocean temperatures escalate by varying the heat source parameter. Additionally, these newly established techniques demonstrate predictability.</abstract>

A modification of explicit time integrator scheme for unsteady power-law nanofluid flow over the moving sheets

2024-01-26

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +2 more

This paper introduces an exponential time integrator scheme for solving partial differential equations in time, specifically addressing the scalar time-dependent convection-diffusion equation. The proposed second-order accurate scheme is demonstrated to … This paper introduces an exponential time integrator scheme for solving partial differential equations in time, specifically addressing the scalar time-dependent convection-diffusion equation. The proposed second-order accurate scheme is demonstrated to be stable. It is applied to analyze the heat and mass transfer mixed convective flow of power-law nanofluid over flat and oscillatory sheets. The governing equations are transformed into a dimensionless set of partial differential equations, with the continuity equation discretized using a first-order scheme. The proposed time integrator scheme is employed in the time direction, complemented by second-order central discretization in the space direction for the momentum, energy, and nanoparticle volume fraction equations. Quantitative results indicate intriguing trends, indicating that an increase in the Prandtl number and thermophoresis parameter leads to a decrease in the local Nusselt number. This modified time integrator is a valuable tool for exploring the dynamics of unsteady power-law nanofluid flow over moving sheets across various scenarios. Its versatility extends to the examination of unstable fluid flows. This work improves engineering and technological design and operation in nanofluid dynamics. Improving numerical simulations’ precision and computational efficiency deepens our comprehension of fundamental physics, yielding helpful information for enhancing systems that rely on nanofluids.

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A Third-order Two Stage Numerical Scheme and Neural Network Simulations for SEIR Epidemic Model: A Numerical Study

2024-02-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

This study focuses on the cutting-edge field of epidemic modeling, providing a comprehensive investigation of a third-order two-stage numerical approach combined with neural network simulations for the SEIR (Susceptible-Exposed-Infectious-Removed) epidemic … This study focuses on the cutting-edge field of epidemic modeling, providing a comprehensive investigation of a third-order two-stage numerical approach combined with neural network simulations for the SEIR (Susceptible-Exposed-Infectious-Removed) epidemic model. An explicit numerical scheme is proposed in this work for dealing with both linear and nonlinear boundary value problems. The scheme is built on two grid points, or two time levels, and is third-order. The main advantage of the scheme is its order of accuracy in two stages. Third-order precision is not only not provided by most existing explicit numerical approaches in two phases, but it also necessitates the computation of an additional derivative of the dependent variable. The proposed scheme's consistency and stability are also examined and presented. Nonlinear SEIR (susceptible-exposed-infected-recovered) models are used to implement the scheme. The scheme is compared with the non-standard finite difference and forward Euler methods that are already in use. The graph shows that the plan is more accurate than non-standard finite difference and forward Euler methods that are already in use. The solution obtained is then looked at through the lens of the neural network. The neural network is trained using an optimization approach known as the Levenberg-Marquardt backpropagation (LMB) algorithm. The mean square error across the total number of iterations, error histograms, and regression plots are the various graphs that can be created from this process. This work conducts thorough evaluations to not only identify the strengths and weaknesses of the suggested approach but also to examine its implications for public health intervention. The results of this study make a valuable contribution to the continuously developing field of epidemic modeling. They emphasize the importance of employing modern numerical techniques and machine learning algorithms to enhance our capacity to predict and effectively control infectious diseases. Doi: 10.28991/ESJ-2024-08-01-023 Full Text: PDF

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Precision in disease dynamics: Finite difference solutions for stochastic epidemics with treatment cure and partial immunity

2024-03-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

The complex and ever-changing characteristics of epidemic modelling, particularly when considering random elements, provide a substantial obstacle in creating precise and practical numerical methods for solving differential equations. This study … The complex and ever-changing characteristics of epidemic modelling, particularly when considering random elements, provide a substantial obstacle in creating precise and practical numerical methods for solving differential equations. This study contributes to this effort by introducing an innovative finite difference method for linear and non-linear stochastic and deterministic differential equations. This scheme expands explicitly upon the Euler Maruyama method, improving its precision for the deterministic aspect while ensuring coherence in dealing with stochastic terms. This contribution provides a numerical scheme that can be used to find solutions to linear and non-linear stochastic and deterministic differential equations. The scheme can be considered as the extension of the Euler Maruyama scheme for solving stochastic differential equations. The Euler Maruyama scheme offers a first-order accuracy of the deterministic model. Still, this scheme provides second-order accuracy for the deterministic part, whereas the integration of stochastic terms is the same in both schemes. The scheme is employed in a stochastic diffusive epidemic model with the effect of treatment, cure, and partial immunity. The comparison of the proposed scheme with the existing nonstandard finite difference method is made, and it is shown that the proposed scheme performs better than the nonstandard finite difference method in accuracy for the deterministic differential equations. It is also demonstrated that susceptible people rise whereas infected and recovered people decline by enhancing treatment cure rate. How does the cure rate of the treatment influence the number of the three populations, i.e., S(t), I(t), and R(t)? The results from the numerical simulation have provided useful insights into the dynamics of the epidemic model under various settings. This is particularly useful for influencing any public health plan and intervention. Thus, this work contributes numerical approaches and is an essential tool for epidemiological studies.

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

2024-05-06

Yasir Nawaz , Muhammad Shoaib Arif , Muavia Mansoor +2 more

An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order … An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid’s fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme.

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Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources

2024-01-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

Abstract Scientific inquiry into effective numerical methods for modelling complex physical processes has led to the investigation of fluid dynamics, mainly when non-Newtonian properties and complex heat sources are involved. … Abstract Scientific inquiry into effective numerical methods for modelling complex physical processes has led to the investigation of fluid dynamics, mainly when non-Newtonian properties and complex heat sources are involved. This paper presents an enhanced exponential time integrator approach to dynamically simulate non-Newtonian boundary layer flow with spatially and temporally varying heat sources. We propose an explicit scheme with second-order accuracy in time, demonstrated to be stable through Fourier series analysis, for solving time-dependent partial differential equations (PDEs). Utilizing this scheme, we construct and solve dimensionless PDEs representing the flow of Williamson fluid under the influence of space- and temperature-dependent heat sources. The scheme discretizes the continuity equation of incompressible fluid and Navier–Stokes, energy, and concentration equations using the central difference in space. Our analysis illuminates how factors affect velocity, temperature, and concentration profiles. Specifically, we observe a rise in temperature profile with enhanced coefficients of space and temperature terms in the heat source. Non-Newtonian behaviours and geographical/temporal variations in heat sources are critical factors influencing overall dynamics. The novelty of our work lies in developing an explicit exponential integrator approach, offering stability and second-order accuracy, for solving time-dependent PDEs in non-Newtonian boundary layer flow with variable heat sources. Our results provide valuable quantitative insights for understanding and controlling complex fluid dynamics phenomena. By addressing these challenges, our study advances numerical techniques for modelling real-world systems with implications for various engineering and scientific applications.

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Unique Fixed Point Results via Geraghty Type Contraction with Applications

2025-05-01

Kamaleldin Abodayeh , Badshah-e- Rome , Sidra Nizam +1 more

In this research work, using the concept of Banach contraction principle and Geraghty type contractions, some unique fixed point results are established in the context of $\mu$-extended fuzzy b-metric spaces. … In this research work, using the concept of Banach contraction principle and Geraghty type contractions, some unique fixed point results are established in the context of $\mu$-extended fuzzy b-metric spaces. The developed results are applied to ensure the existence of solution to integral equation and non-linear fractional order differential equation.

Mathematical Modeling with Two Strains to Investigate Evolution of COVID-19 from Computational and Theoretical Perspectives

2025-05-01

Muhammad Bilal Riaz , Zeeshan Ali , Rahim Ud Din +3 more

The respiratory disease COVID-19 is brought on by a mutagenic {ribonucleic acid (RNA)} virus. Variants with various traits that could potentially impact transmissibility started to appear globally in December 2020. … The respiratory disease COVID-19 is brought on by a mutagenic {ribonucleic acid (RNA)} virus. Variants with various traits that could potentially impact transmissibility started to appear globally in December 2020. We develop and examine a computational model of two-strain COVID-19 transmission behaviors in order to deal with this novel aspect of the disease. After a theoretical analysis, enough criteria are derived for the stability of the model's equilibrium. The model contains single-strain 1 and variant 2 endemic equilibria as well as disease-free and endemic equilibria. The global stability of the model equilibrium is demonstrated using the Lyapunov function. For each strain, we separately compute the basic reproductive numbers $\mathscr{R}_{01} <1$, and $\mathscr{R}_{02}<1$. To determine the realistic values of the model parameters, the actual data from South Africa for the period of three months, are taken into consideration.Sensitivity study employing the {partial rank correlation coefficient technique (PRCC)} to look into the key variables that affect $\mathscr{R}_{01} <1$, or $\mathscr{R}_{02}<1$ decrease or increase. We show the numerical simulation of the model using {non-standard finite difference scheme (NSFDS)} and Caputo fractional derivative for distinct non-integer order. The world health organizations (WHO) recommends {standard operating procedures (SOPs)} to minimize infection in the population. Based on these recommendations, some graphical results for the model with sensitive parameters are provided.

An Innovative Analytical Result of Two-Dimensional Heat Equation Using Joint Mechanism of Natural Transform and Adomian Decomposition Method

2025-05-01

Muhammad Usman , Hidayat Ullah Khan , Muhammad Sarwar +2 more

This research article has put forward an innovative analytical result of the 2D heat equation having a source term. The aforesaid non-homogenous PDE is solved through a new hybrid mechanism. … This research article has put forward an innovative analytical result of the 2D heat equation having a source term. The aforesaid non-homogenous PDE is solved through a new hybrid mechanism. whereas the technique supports the solution process, commencing with the parametric form of the 2D heat equation. Furthermore, this hybrid mechanism which consists of Natural transform (NT) and a series solution method of Adomian decomposition method (ADM) is applied properly. Next, the solution that is obtained for the unknown function is presented in series form. During the computational process, it was observed that the proposed mechanism is less time-consuming and efficient with accurate results. Which shows that the mechanism (proposed mechanism) makes a very useful contribution to the analytical solution of the 2D heat equation. The paper is properly supported with appropriate examples to verify the claim.

A Computational Scheme of Exponential Integrator for Fuzzy Electrical Boundary Layer Flow with Variable Viscosity and Thermal Conductivity

2024-12-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

Solutionsof Fuzzy Goursat Problems with Generalized Hukuhara (gH)-Differentiability Concept

2024-09-20

Noor Jamal , Muhammad Sarwar , Kamaleldin Abodayeh +3 more

In this manuscript, we will discuss the solutions of Goursat problems with fuzzy boundary conditions involving gH-differentiability. The solutions to these problems face two main challenges. The first challenge is … In this manuscript, we will discuss the solutions of Goursat problems with fuzzy boundary conditions involving gH-differentiability. The solutions to these problems face two main challenges. The first challenge is to deal with the two types of fuzzy gH-differentiability: (i)-differentiability and (ii)-differentiability. The sign of coefficients in Goursat problems and gH-differentiability produces sixteen possible cases. The existing literature does not afford a solution method that addresses all the possible cases of this problem. The second challenge is the mixed derivative term in Goursat problems with fuzzy boundary conditions. Therefore, we propose to discuss the solutions of fuzzy Goursat problems with gH-differentiability. We will discuss the solutions of fuzzy Goursat problems in series form with natural transform and Adomian decompositions. To demonstrate the usability of the established solution methods, we will provide some numerical examples.

Classification of Random Walks and Green’s Theorem on Infinite Homogeneous Trees

2024-08-15

P. Swarnambigai , N. Nathiya , K. Kalaivani +1 more

In the context of random walks whose states are the vertices of an infinite tree, a classification of random walks is given as transient or recurrent. On the infinite homogeneous … In the context of random walks whose states are the vertices of an infinite tree, a classification of random walks is given as transient or recurrent. On the infinite homogeneous trees with the assumption that the transition probability between any two neighboring states are the same, a form of the classical Green’s formula is derived. As a consequence, two versions of the mean-value property for median functions are obtained.

Ϝ-Contraction of Hardy–Rogers type in supermetric spaces with applications

2024-07-08

Kamaleldin Abodayeh , Syed Khayyam Shah , Muhammad Sarwar +2 more

Abstract This article focuses on studying some fixed-point results via Ϝ -contraction of Hardy–Rogers type in the context of supermetric space and ordered supermetric space. We also introduced rational-type z … Abstract This article focuses on studying some fixed-point results via Ϝ -contraction of Hardy–Rogers type in the context of supermetric space and ordered supermetric space. We also introduced rational-type z -contraction on supermetric space. For authenticity, some illustrative examples and applications have been included.

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Ćirić-type generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e23"><mml:mi>F</mml:mi></mml:math>-contractions with integral inclusion in super metric spaces

2024-06-18

Kamaleldin Abodayeh , Syed Khayyam Shah , Muhammad Sarwar +2 more

This study aims to explore Ćirić-type generalized F-contractions, almost F-contractions, and the combination of these contractions in the framework of super metric spaces. These generalizations are significant because they hold … This study aims to explore Ćirić-type generalized F-contractions, almost F-contractions, and the combination of these contractions in the framework of super metric spaces. These generalizations are significant because they hold where the usual metric conditions mayn't be fulfilled. Using the iteration method, fixed point results have been obtained for these contractions, and through examples and applications to integral inclusions and contractions, we extend existing literature significantly. This extension offers new insights and demonstrates practical relevance.

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

2024-05-06

Yasir Nawaz , Muhammad Shoaib Arif , Muavia Mansoor +2 more

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Existence and Uniqueness Result for Fuzzy Fractional Order Goursat Partial Differential Equations

2024-04-25

Muhammad Sarwar , Noor Jamal , Kamaleldin Abodayeh +2 more

In this manuscript, we discuss fractional fuzzy Goursat problems with Caputo’s gH-differentiability. The second-order mixed derivative term in Goursat problems and two types of Caputo’s gH-differentiability pose challenges to dealing … In this manuscript, we discuss fractional fuzzy Goursat problems with Caputo’s gH-differentiability. The second-order mixed derivative term in Goursat problems and two types of Caputo’s gH-differentiability pose challenges to dealing with Goursat problems. Therefore, in this study, we convert Goursat problems to equivalent systems fuzzy integral equations to deal properly with the mixed derivative term and two types of Caputo’s gH-differentiability. In this study, we utilize the concept of metric fixed point theory to discuss the existence of a unique solution of fractional fuzzy Goursat problems. For the useability of established theoretical work, we provide some numerical problems. We also discuss the solutions to numerical problems by conformable double Laplace transform. To show the validity of the solutions we provide 3D plots. We discuss, as an application, why fractional partial fuzzy differential equations are the generalization of usual partial fuzzy differential equations by providing a suitable reason. Moreover, we show the advantages of the proposed fractional transform over the usual Laplace transform.

Controllability of Hilfer fractional neutral impulsive stochastic delayed differential equations with nonlocal conditions

2024-04-22

Sadam Hussain , Muhammad Sarwar , Kamaleldin Abodayeh +2 more

In this paper, the controllability for Hilfer fractional neutral stochastic differential equations with infinite delay and nonlocal conditions has been investigated. Using concepts from fractional calculus, semigroup of operators, fixed-point … In this paper, the controllability for Hilfer fractional neutral stochastic differential equations with infinite delay and nonlocal conditions has been investigated. Using concepts from fractional calculus, semigroup of operators, fixed-point theory, measures of noncompactness, and stochastic theory the main controllability conclusion is attained. The applications of the key findings are finally illustrated with two examples.

Application of Darbo-type generalized θ-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="script">F</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">ℵ</mml:mi></mml:mrow></mml:msub></mml:math>-contractions to the fractional order Lymphatic filariasis infection model

2024-04-10

Mian Bahadur Zada , Haroon Rashid , Muhammad Sarwar +1 more

This work presents a significant contribution to the field of mathematical analysis by introducing θ-Fℵ-contractions of Darbo-type. These newly introduced contractions serve as pivotal tools within our study. By employing … This work presents a significant contribution to the field of mathematical analysis by introducing θ-Fℵ-contractions of Darbo-type. These newly introduced contractions serve as pivotal tools within our study. By employing these contractions, we systematically establish several pivotal fixed point theorems that allow us to guarantee the existence of fixed points in the Banach spaces. We construct particular examples in order to support the validity and effectiveness of our theoretical results. Moreover, we extend the utility of our established theorems by applying them to solve real-world problems. Specifically, we direct our attention to exploring the existence of solutions to the fractional order Lymphatic filariasis infection model.

Controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via Atangana-Baleanu Caputo fractional derivative

2024-03-26

Muhammad Sarwar , Sadam Hussain , Kamaleldin Abodayeh +2 more

On a new generalization of a Perov-type F-contraction with application to a semilinear operator system

2024-03-18

Muhammad Sarwar , Syed Khayyam Shah , Kamaleldin Abodayeh +2 more

Abstract This manuscript aims to present new results about the generalized F -contraction of Hardy–Rogers-type mappings in a complete vector-valued metric space, and to demonstrate the fixed-point theorems for single … Abstract This manuscript aims to present new results about the generalized F -contraction of Hardy–Rogers-type mappings in a complete vector-valued metric space, and to demonstrate the fixed-point theorems for single and pairs of generalized F -contractions of Hardy–Rogers-type mappings. The established results represent a significant development of numerous previously published findings and results in the existing body of literature. Furthermore, to ensure the practicality and effectiveness of our findings across other fields, we provide an application that demonstrates a unique solution for the semilinear operator system within the Banach space.

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Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

2024-03-12

Esam Y. Salah , Bhausaheb Sontakke , Mohammed S. ‬Abdo +3 more

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Precision in disease dynamics: Finite difference solutions for stochastic epidemics with treatment cure and partial immunity

2024-03-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

A Third-order Two Stage Numerical Scheme and Neural Network Simulations for SEIR Epidemic Model: A Numerical Study

2024-02-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

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A modification of explicit time integrator scheme for unsteady power-law nanofluid flow over the moving sheets

2024-01-26

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +2 more

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A Hybrid SIR-Fuzzy Model for Epidemic Dynamics: A Numerical Study

2024-01-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

This study focuses on the urgent requirement for improved accuracy in disease modeling by introducing a new computational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered (SIR) model … This study focuses on the urgent requirement for improved accuracy in disease modeling by introducing a new computational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered (SIR) model with fuzzy logic, our method effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters.The main aim of this research is to provide a model for disease transmission using fuzzy theory, which can successfully address uncertainty in mathematical modeling.Our main emphasis is on the imprecise transmission rate parameter, utilizing a three-part description of its membership level.This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models.We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis, providing insight into the complex correlation between model parameters and epidemic results.In order to facilitate a quantitative analysis of the fuzzy model, we propose the implementation of a resilient numerical scheme.The convergence study of the scheme demonstrates its trustworthiness, providing a conditionally positive solution, which represents a significant improvement compared to current forward Euler schemes.The numerical findings demonstrate the model's effectiveness in accurately representing the dynamics of disease transmission.Significantly, when the mortality coefficient rises, both the susceptible and infected populations decrease, highlighting the model's sensitivity to important epidemiological factors.Moreover, there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected, as well as an increase in the number of susceptible individuals.This correlation offers a significant understanding of how many elements affect the consequences of an epidemic.Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model.Our approach not only tackles the existing constraints in disease modeling, but also paves the way for additional investigation, providing a vital instrument for researchers and policymakers alike.

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Existence of solution for fractional differential equations involving symmetric fuzzy numbers

2024-01-01

Muhammad Sarwar , Noor Jamal , Kamaleldin Abodayeh +3 more

<abstract>Linear correlated fractional fuzzy differential equations (LCFFDEs) are one of the best tools for dealing with physical problems with uncertainty. The LCFFDEs mostly do not have unique solutions, especially if … <abstract>Linear correlated fractional fuzzy differential equations (LCFFDEs) are one of the best tools for dealing with physical problems with uncertainty. The LCFFDEs mostly do not have unique solutions, especially if the basic fuzzy number is symmetric. The LCFFDEs of symmetric basic fuzzy numbers extend to the new system by extension and produce many solutions. The existing literature does not have any criteria to ensure the existence of unique solutions to LCFFDEs. In this study, we will explore the main causes of the extension and the unavailability of unique solutions. Next, we will discuss the existence and uniqueness conditions of LCFFDEs by using the concept of metric fixed point theory. For the useability of established results, we will also provide numerical examples and discuss their unique solutions. To show the authenticity of the solutions, we will also provide 2D and 3D plots of the solutions.</abstract>

Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources

2024-01-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

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Krasnoselskii type coupled fixed point results and its applications in Banach spaces

2024-01-01

Kamaleldin Abodayeh , Mian Bahadur Zada , Muhammad Sarwar +2 more

In this study, we developed certain coupled fixed point results in a Banach space using fixed point results of the Krasnoselskii type. We provided a result for the existence of … In this study, we developed certain coupled fixed point results in a Banach space using fixed point results of the Krasnoselskii type. We provided a result for the existence of a solution to the system of Caputo-Fabrizio fractional order differential equations using the established coupled fixed point results. To validate the existence result, an example was constructed.

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Modelling Infectious Disease Dynamics: A Robust Computational Approach for Stochastic SIRS with Partial Immunity and an Incidence Rate

2023-11-27

Amani S. Baazeem , Yasir Nawaz , Muhammad Shoaib Arif +2 more

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A two-stage multi-step numerical scheme for mixed convective Williamson nanofluid flow over flat and oscillatory sheets

2023-08-19

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +1 more

Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study

2023-05-27

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

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Numerical Schemes for Fractional Energy Balance Model of Climate Change with Diffusion Effects

2023-05-03

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

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New Iterative Scheme Involving Self-Adaptive Method for Solving Mixed Variational Inequalities

2023-03-20

Aiman Mukheimer , Saleem Ullah , Muhammad Bux +2 more

Variational inequalities (VI) problems have been generalized and expanded in various ways. The VI principle has become a remarkable study area combining pure and applied research. The study of variational … Variational inequalities (VI) problems have been generalized and expanded in various ways. The VI principle has become a remarkable study area combining pure and applied research. The study of variational inequality in mathematics is significantly aided by providing an important framework by fixed-point theory. The concept of fixed-point theory can be considered an inherent component of the VI. We consider a mixed variational inequality (MVI) a useful generalization of a classical variational inequality. The projection method is not applicable to solve MVI due to the involvement of the nonlinear term ϕ. MVI is equivalent to fixed-point problems and the resolvent equation techniques. This technique is commonly used in the research on the existence of a solution to the MVI. This paper uses a new self-adaptive method using step size to modify the fixed-point formulation for solving the MVI. We will also provide the convergence of the proposed scheme. Our output could be seen as a significant refinement of the previously known results for MVI. A numerical example is also provided for the implementation of the generated algorithm.

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Applying an Extended β-ϕ-Geraghty Contraction for Solving Coupled Ordinary Differential Equations

2023-03-14

Hasanen A. Hammad , Kamaleldin Abodayeh , Wasfı Shatanawi

In this paper, we introduce a new class of mappings called “generalized β-ϕ-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the … In this paper, we introduce a new class of mappings called “generalized β-ϕ-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and unite several findings known in the literature. We also provide some examples to support and illustrate our theoretical results. Furthermore, we apply our results to discuss the existence and uniqueness of a solution to a coupled ordinary differential equation as an application of our finding.

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Predictor–Corrector Scheme for Electrical Magnetohydrodynamic (MHD) Casson Nanofluid Flow: A Computational Study

2023-01-16

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

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New Exact Solutions of Landau-Ginzburg-Higgs Equation Using Power Index Method

2023-01-12

Khalil Ahmad , Khudija Bibi , Muhammad Shoaib Arif +1 more

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Stability Analysis of Fractional-Order Predator-Prey System with Consuming Food Resource

2023-01-07

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Asad Ejaz

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Solving singular equations of length eight over torsion-free groups

2023-01-01

Mairaj Bibi , Sajid Ali , Muhammad Shoaib Arif +1 more

<abstract>It was demonstrated by Bibi and Edjvet in [<xref ref-type="bibr" rid="b1">1</xref>] that any equation with a length of at most seven over torsion-free group can be solvable. This corroborates Levin's … <abstract>It was demonstrated by Bibi and Edjvet in [<xref ref-type="bibr" rid="b1">1</xref>] that any equation with a length of at most seven over torsion-free group can be solvable. This corroborates Levin's [<xref ref-type="bibr" rid="b2">2</xref>] assertion that any equation over a torsion-free group is solvable. It is demonstrated in this article that a singular equation of length eight over torsion-free groups is solvable.</abstract>

Computational Modeling of Reaction-Diffusion COVID-19 Model Having Isolated Compartment

2022-07-12

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Asad Ejaz

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A Computational Approach to a Mathematical Model of Climate Change Using Heat Sources and Diffusion

2022-07-01

Muhammad Shoaib Arif , Kamaleldin Abodayeh , Yasir Nawaz

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A Third-Order Two-Stage Numerical Scheme for Fractional Stokes Problems: A Comparative Computational Study

2022-06-14

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

An <scp>Explicit‐Implicit</scp> Numerical Scheme for Time Fractional Boundary Layer Flows

2022-06-01

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

This contribution is concerned with constructing a fractional explicit-implicit numerical scheme for solving time-dependent partial differential equations. The proposed scheme has the advantage over some existing explicit in providing better … This contribution is concerned with constructing a fractional explicit-implicit numerical scheme for solving time-dependent partial differential equations. The proposed scheme has the advantage over some existing explicit in providing better stability region. But it has one of its limitations of being conditionally stable, even having one implicit stage. For spatial discretization, a fourth-order compact scheme is considered. The stability and convergence of the proposed scheme for respectively the scalar parabolic equation and system of parabolic equations are given. For the sake of application of the scheme, fractional models of flow between parallel plates and mixed convection flow of Stokes' problems under the effects of viscous dissipation and thermal radiation are constructed. The proposed scheme for the classical model is also compared with built-in Matlab solver pdepe for solving parabolic and elliptic equations and existing numerical schemes. It is found that Matlab solver pdepe is failed to find the solution of the considered flow problem with larger values of Eckert number or coefficient of the nonlinear term. But, the proposed scheme successfully finds the solution for classical and fractional models and shows faster convergence than the existing scheme. We provide illustrative computer simulations to show the principal computational features of this approach.

A Compact Numerical Scheme for the Heat Transfer of Mixed Convection Flow in Quantum Calculus

2022-05-13

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

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A Numerical Scheme for Fractional Mixed Convection Flow Over Flat and Oscillatory Plates

2022-05-03

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

A Self-Adaptive Technique for Solving Variational Inequalities: A New Approach to the Problem

2022-04-26

Muhammad Bux , Saleem Ullah , Muhammad Shoaib Arif +1 more

Variational inequalities are considered the most significant field in applied mathematics and optimization because of their massive and vast applications. The current study proposed a novel iterative scheme developed through … Variational inequalities are considered the most significant field in applied mathematics and optimization because of their massive and vast applications. The current study proposed a novel iterative scheme developed through a fixed-point scheme and formulation for solving variational inequalities. Modification is done by using the self-adaptive technique that provides the basis for predicting a new predictor-corrector self-adaptive for solving nonlinear variational inequalities. The motivation of the presented study is to provide a meaningful extension to existing knowledge through convergence at mild conditions. The numerical interpretation provided a significant boost to the results.

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Self-Adaptive Predictor-Corrector Approach for General Variational Inequalities Using a Fixed-Point Formulation

2022-03-12

Kubra Sanaullah , Saleem Ullah , Muhammad Shoaib Arif +2 more

A literature review revealed that the general variational inequalities, fixed-point problems, and Winner–Hopf equations are equivalent. In this study, general variational inequality and fixed-point problem are considered. We introduced a … A literature review revealed that the general variational inequalities, fixed-point problems, and Winner–Hopf equations are equivalent. In this study, general variational inequality and fixed-point problem are considered. We introduced a new iterative method based on a self-adaptive predictor-corrector approach for finding a solution to the GVI. Adaptations in the fixed-point formulation and self-adaptive techniques have been used to predict a novel iterative approach. Convergence analyses of the suggested algorithm are demonstrated. Moreover, numerical analysis shows that we establish the new best method for solving general variational inequality which performs better than the previous one. Furthermore, it is known that GVI consisted of several classes including variational inequalities and related optimization problems, and results obtained in this study continue to hold for these problems.

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An explicit‐implicit numerical scheme for time fractional boundary layer flows

2022-03-10

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

Solution of differential equations with infinite delay via coupled fixed point

2022-01-31

K. Mebarki , Ahmed Boudaoui , Wasfı Shatanawi +2 more

This manuscript aims to prove exciting results that unify and generalize several fixed point results for metric spaces endowed with graphs. As an application, we apply our own results to … This manuscript aims to prove exciting results that unify and generalize several fixed point results for metric spaces endowed with graphs. As an application, we apply our own results to give and introduce sufficient conditions to guarantee existence solutions of such differential equations with infinite delay.

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Stability Analysis of Predator-Prey System with Consuming Resource and Disease in Predator Species

2022-01-01

Asad Ejaz , Yasir Nawaz , Muhammad Shoaib Arif +2 more

Certain dynamic iterative scheme families and multi-valued fixed point results

2022-01-01

Amjad Ali , Muhammad Arshad , Eskandar Emeer +3 more

Finite difference schemes for time-dependent convection q-diffusion problem

2022-01-01

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +1 more

Periodic and fixed points for $ F $-type contractions in $ b $-gauge spaces

2022-01-01

Nosheen Zikria , Aiman Mukheimer , Maria Samreen +3 more

<abstract>In this paper, we introduce $ \mathcal{J}_{s; \Omega} $-families of generalized pseudo-$ b $-distances in $ b $-gauge spaces $ (U, {Q}_{s; \Omega}) $. Moreover, by using these $ \mathcal{J}_{s; … <abstract>In this paper, we introduce $ \mathcal{J}_{s; \Omega} $-families of generalized pseudo-$ b $-distances in $ b $-gauge spaces $ (U, {Q}_{s; \Omega}) $. Moreover, by using these $ \mathcal{J}_{s; \Omega} $-families on $ U $, we define the $ \mathcal{J}_{s; \Omega} $-sequential completeness and construct an $ F $-type contraction $ T:U\rightarrow U $. Furthermore, we develop novel periodic and fixed point results for these mappings in the setting of $ b $-gauge spaces using $ \mathcal{J}_{s; \Omega} $-families on $ U $, which generalize and improve some of the results in the corresponding literature. The validity and importance of our theorems are shown through an application via an existence solution of an integral equation.</abstract>

Existence and Uniqueness Results of Coupled Fractional-Order Differential Systems Involving Riemann–Liouville Derivative in the Space Wa+γ1,1(a,b)×Wa+γ2,1(a,b) with Perov’s Fixed Point Theorem

2021-11-13

Noura Laksaci , Ahmed Boudaoui , Kamaleldin Abodayeh +2 more

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Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions

2021-11-03

Saleh S. Redhwan , Sadikali L. Shaikh , Mohammed S. ‬Abdo +4 more

Generalized proportional fractional integral functional bounds in Minkowski’s inequalities

2021-09-17

Tariq A. Aljaaidi , Deepak B‎. ‎Pachpatte , Wasfı Shatanawi +2 more

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An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

2021-08-03

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh +1 more

Coauthor	Papers Together
Muhammad Shoaib Arif	29
Wasfı Shatanawi	22
Yasir Nawaz	21
Muhammad Sarwar	12
Thabet Abdeljawad	7
Thanin Sitthiwirattham	7
Victor Anandam	6
Aiman Mukheimer	6
Nabil Mlaiki	6
Mohammed S. ‬Abdo	5
Ahmed Boudaoui	4
Chanon Promsakon	4
Jehad Alzabut	4
T. Barakat	3
Hassen Aydi	3
Syed Khayyam Shah	3
Saleem Ullah	3
Nizar Souayah	3
Muhib Abuloha	3
K. Mebarki	3
Noor Jamal	3
Asad Ejaz	3
Mairaj Bibi	3
Taqi A. M. Shatnawi	2
Manel Hleili	2
Doaa Rizk	2
Muhammad Bux	2
Atif Hassan Soori	2
Ariana Pitea	2
Mian Bahadur Zada	2
Omar M. Aldossary	2
A. Pokrovskii	2
Mohammed A. ‬Almalahi	2
Amani S. Baazeem	2
Anwar Bataihah	2
Tariq A. Aljaaidi	2
D. Vignesh	1
B. Abdallah	1
Fawad Ali	1
Daoud S. Mashat	1
Mdi Begum Jeelani	1
Rahim Ud Din	1
Hidayat Ullah Khan	1
Sadam Hussain	1
İshak Altun	1
Kubra Sanaullah	1
Jagan Mohan Jonnalagadda	1
Khalil Ahmad	1
Bhausaheb Sontakke	1
N. Nathiya	1

Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales

1922-01-01

Stefan Banach

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Fixed points of a new type of contractive mappings in complete metric spaces

2012-06-07

Dariusz Wardowski

In the article, we introduce a new concept of contraction and prove a fixed point theorem which generalizes Banach contraction principle in a different way than in the known results … In the article, we introduce a new concept of contraction and prove a fixed point theorem which generalizes Banach contraction principle in a different way than in the known results from the literature. The article includes an example which shows the validity of our results, additionally there is delivered numerical data which illustrates the provided example. MSC: 47H10; 54E50

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New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model

2016-01-01

Abdon Atangana , Dumitru Băleanu

In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional … In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.

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Modified class of explicit and enhanced stability region schemes: Application to mixed convection flow in a square cavity with a convective wall

2020-12-11

Yasir Nawaz , Muhammad Shoaib Arif

Abstract A modification of Adams–Bashforth methods is given to construct time discretization schemes for partial differential equations. The second‐order modified method is shown to have a larger stability region than … Abstract A modification of Adams–Bashforth methods is given to construct time discretization schemes for partial differential equations. The second‐order modified method is shown to have a larger stability region than second‐order standard Adams–Bashforth for the two‐dimensional heat equation. Later the scheme is applied on considered flow problem in a square cavity. The flow problem is a modified mathematical model of the heat and mass transfer of mixed convection flow in a square cavity with effects of the inclined magnetic field and thermal radiations. In addition to this, another feature of the present contribution is to apply the coupling approach for employing a mixture of stable and unstable schemes. This coupling approach is based upon the difference quotient that has been used in the literature to construct flux limiters for reducing oscillations in the discontinuous solutions of hyperbolic conservation laws. Since proposed scheme produces oscillation in the beginning and then diverges for the chosen diffusion number that falls in the unstable region, so these oscillations, due to instability, is reduced by coupling it with the scheme that can produce the convergent solution. The convergence of the proposed scheme for the considered modified nondimensional mathematical model of mixed convection flow is also given. The improvement is shown in graphs when proposed second order in time scheme is compared with the standard second order in time Adams–Bashforth method. Also, the mixture of first‐order and unconditionally unstable Richardson's schemes is applied, and the solution is obtained, and some plots are provided.

Fixed points for generalized weakly contractive mappings in partial metric spaces

2011-07-24

Thabet Abdeljawad

Theory and Applications of Fractional Differential Equations

2006-01-01

Anatoly A. Kilbas , H. M. Srivastava , Juan J. Trujillo

Some coupled fixed point theorems in quasi-partial metric spaces

2013-06-11

Wasfı Shatanawi , Ariana Pitea

In this paper, we study some coupled fixed point results in a quasi-partial metric space. Also, we introduce some examples to support the useability of our results. MSC:47H10, 54H25. In this paper, we study some coupled fixed point results in a quasi-partial metric space. Also, we introduce some examples to support the useability of our results. MSC:47H10, 54H25.

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An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow

2021-06-09

Yasir Nawaz , Muhammad Shoaib Arif , Wasfı Shatanawi +1 more

The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). The proposed explicit scheme has an advantage over the corresponding … The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). The proposed explicit scheme has an advantage over the corresponding implicit compact scheme to find solutions of nonlinear and linear convection–diffusion type equations because the implicit existing compact scheme fails to obtain the solution. In addition, the present scheme provides fourth-order accuracy in space and second-order accuracy in time, and is constructed on three grid points and three time levels. It is a compact multistep scheme and conditionally stable, while the existing multistep scheme developed on three time levels is unconditionally unstable for parabolic and considered a type of equations. The mathematical model of the heat transfer in a mixed convective radiative fluid flow over a flat plate is also given. The convergence conditions of dimensionless forms of these equations are given, and also the proposed scheme solves equations, and results are compared with two existing schemes. It is hoped that the results in the current report are a helpful source for future fluid-flow studies in an industrial environment in an enclosure area.

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A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology

2022-01-31

Yasir Nawaz , Muhammad Shoaib Arif , Wasfı Shatanawi

In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than … In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than the corresponding model of fractional ordinary differential equations (ODEs). The Caputo fractional derivative is considered. Linear stability analysis of the disease-free equilibrium state of the epidemic model (ODEs) is presented by employing Routh–Hurwitz stability criteria. In order to solve this model, a fractional numerical scheme is proposed. The proposed scheme can be used to find conditions for obtaining positive solutions for diffusive epidemic models. The stability of the scheme is given, and convergence conditions are found for the system of the linearized diffusive fractional epidemic model. In addition to this, the deficiencies of accuracy and consistency in the nonstandard finite difference method are also underlined by comparing the results with the standard fractional scheme and the MATLAB built-in solver pdepe. The proposed scheme shows an advantage over the fractional nonstandard finite difference method in terms of accuracy. In addition, numerical results are supplied to evaluate the proposed scheme’s performance.

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Fixed point theorems in partially ordered metric spaces and applications

2006-04-05

T. Gnana Bhaskar , V. Lakshmikantham

Controlled Metric Type Spaces and the Related Contraction Principle

2018-10-08

Nabil Mlaiki , Hassen Aydi , Nizar Souayah +1 more

In this article, we introduce a new extension of b-metric spaces, called controlled metric type spaces, by employing a control function α ( x , y ) of the right-hand … In this article, we introduce a new extension of b-metric spaces, called controlled metric type spaces, by employing a control function α ( x , y ) of the right-hand side of the b-triangle inequality. Namely, the triangle inequality in the new defined extension will have the form, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + α ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Examples of controlled metric type spaces that are not extended b-metric spaces in the sense of Kamran et al. are given to show that our extension is different. A Banach contraction principle on controlled metric type spaces and an example are given to illustrate the usefulness of the structure of the new extension.

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A fixed point theorem for set-valued quasi-contractions in b-metric spaces

2012-05-22

Hassen Aydi , Monica-Felicia Bota , Erdal Karapınar +1 more

In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing … In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.

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Potential-theoretic study of functions on an infinite network

2008-02-01

Kamaleldin Abodayeh , Victor Anandam

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Solution of linear correlated fuzzy differential equations in the linear correlated fuzzy spaces

2023-01-01

Noor Jamal , Muhammad Sarwar , Nabil Mlaiki +1 more

<abstract>Linear correlated fuzzy differential equations (LCFDEs) are a valuable approach to handling physical problems, optimizations problems, linear programming problems etc. with uncertainty. But, LCFDEs employed on spaces with symmetric basic … <abstract>Linear correlated fuzzy differential equations (LCFDEs) are a valuable approach to handling physical problems, optimizations problems, linear programming problems etc. with uncertainty. But, LCFDEs employed on spaces with symmetric basic fuzzy numbers often exhibit multiple solutions due to the extension process. This abundance of solutions poses challenges in the existing literature's solution methods for LCFDEs. These limitations have led to reduced applicability of LCFDEs in dealing with such types of problems. Therefore, in the current study, we focus on establishing existence and uniqueness results for LCFDEs. Moreover, we will discuss solutions in the canonical form of LCFDEs in the space of symmetric basic fuzzy number which is currently absent in the literature. To enhance the practicality of our work, we provide examples and plots to illustrate our findings.</abstract>

An explicit‐implicit numerical scheme for time fractional boundary layer flows

2022-03-10

Yasir Nawaz , Muhammad Shoaib Arif , Kamaleldin Abodayeh

A class of second‐order schemes with application to chemically reactive radiative natural convection flow in a rectangular enclosure

2021-07-06

Yasir Nawaz , Muhammad Shoaib Arif , Amna Nazeer

Abstract A new class of explicit second‐order schemes is proposed for solving time‐dependent partial differential equations. This class of proposed schemes is constructed on three‐time levels. Stability is found for … Abstract A new class of explicit second‐order schemes is proposed for solving time‐dependent partial differential equations. This class of proposed schemes is constructed on three‐time levels. Stability is found for the scalar two‐dimensional heat equation and the system of time‐dependent partial differential equations. This partial differential equations system comprises a non‐dimensional set of equations obtained from the governing equations of natural convection chemically reactive fluid flow in a rectangular enclosure with thermal radiations. Flow is generated by applying the force of pressure. Graphs of streamlines, contours plots of velocity, temperature and concentration profiles, local Nusselt number, and local Sherwood number are displayed with the variation of time and parameters in the considered partial differential equations. Results are shown in the form of streamlines and contour plots. It is found that local Nusselt number has dual behavior by enhancing radiation parameter whereas local Sherwood number de‐escalates by upraising the reaction rate parameter. It is hoped that the results in this pagination will serve as a valuable resource for future fluid‐flow studies in an enclosed industrial environment.

On the nonstandard finite difference method for reaction–diffusion models

2022-12-05

Syed Ahmed Pasha , Yasir Nawaz , Muhammad Shoaib Arif

A generalized Banach contraction principle that characterizes metric completeness

2007-12-06

Tomonari Suzuki

We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space. We also discuss the … We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space. We also discuss the Meir-Keeler fixed point theorem.

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On the ψ -Hilfer fractional derivative

2018-01-09

J. Vanterler da C. Sousa , E. Capelas de Oliveira

Existence of positive solutions for weighted fractional order differential equations

2020-10-13

Mohammed S. ‬Abdo , Thabet Abdeljawad , Saeed M. Ali +2 more

Generalized fractional derivatives and Laplace transform

2019-03-21

Fahd Jarad , Thabet Abdeljawad

In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to … In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.

Design of nonstandard computational method for stochastic susceptible–infected–treated–recovered dynamics of coronavirus model

2020-09-18

Wasfı Shatanawi , Ali Raza , Muhammad Shoaib Arif +3 more

Abstract The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of … Abstract The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear stochastic susceptible-infected-treated-recovered system, and we investigate the stochastic reproduction dynamics, both analytically and numerically. We applied different standard and nonstandard computational numerical methods for the solution of the stochastic system. The design of a nonstandard computation method for the stochastic system is innovative. Unfortunately, standard computation numerical methods are time-dependent and violate the structure properties of models, such as positivity, boundedness, and dynamical consistency of the stochastic system. To that end, convergence analysis of nonstandard computational methods and simulation with a comparison of standard computational methods are presented.

Essential Features Preserving Dynamics of Stochastic Dengue Model

2020-12-22

Wasfı Shatanawi , Ali Raza , Muhammad Shoaib Arif +3 more

Nonlinear stochastic modelling plays an important character in the different fields of sciences such as environmental, material, engineering, chemistry, physics, biomedical engineering, and many more. In the current study, we … Nonlinear stochastic modelling plays an important character in the different fields of sciences such as environmental, material, engineering, chemistry, physics, biomedical engineering, and many more. In the current study, we studied the computational dynamics of the stochastic dengue model with the real material of the model. Positivity, boundedness, and dynamical consistency are essential features of stochastic modelling. Our focus is to design the computational method which preserves essential features of the model. The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature. Analysis and comparison were explored in favour of convergence. Also, we address the comparison between the stochastic and deterministic models.

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Ciric type generalized F-contractions on completemetric spaces and fixed point results

2014-01-01

Gülhan Mınak , Asuman Helvacı , İshak Altun

Recently, Wardowski [15] introduced the concept of F-contraction on complete metric space. This type contraction is proper generalization of ordinary contraction. In the present paper, we give some fixed point … Recently, Wardowski [15] introduced the concept of F-contraction on complete metric space. This type contraction is proper generalization of ordinary contraction. In the present paper, we give some fixed point results for generalized F-contractions including Ciric type generalized F-contraction and almost F-contraction on complete metric space. Also, we give some illustrative examples.

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A Generalization of b-Metric Space and Some Fixed Point Theorems

2017-03-23

Tayyab Kamran , Maria Samreen , Qurat Ul Ain

In this paper, inspired by the concept of b-metric space, we introduce the concept of extended b-metric space. We also establish some fixed point theorems for self-mappings defined on such … In this paper, inspired by the concept of b-metric space, we introduce the concept of extended b-metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our results extend/generalize many pre-existing results in literature.

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Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces

2010-12-28

İshak Altun , Ali Erduran

Abstract Matthews (1994) introduced a new distance "Equation missing" on a nonempty set "Equation missing", which … Abstract Matthews (1994) introduced a new distance "Equation missing" on a nonempty set "Equation missing", which is called partial metric. If "Equation missing" is a partial metric space, then "Equation missing" may not be zero for "Equation missing". In the present paper, we give some fixed point results on these interesting spaces.

Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system

2017-04-25

Abdon Atangana

Some fixed point theorems in extended b-metric spaces

2022-01-01

Vildan Öztürk , Duran Türkoğlu , Arslan Hojat Ansari

Banach contraction principle is one of the earlier and main results in fixed point theory. Banach contraction principle which guarantees existence and uniqueness of fixed point was proved in complete … Banach contraction principle is one of the earlier and main results in fixed point theory. Banach contraction principle which guarantees existence and uniqueness of fixed point was proved in complete metric spaces in 1922 by Banach. According to this principle, "let (X, d) be a complete metric space and f : X → X be a mapping. If there exists a constant 0 ≤ k < 1 such that for all x, y ∈ X, d( f x, f y) ≤ k.d(x, y), then f has a unique fixed point". In this work, we define almost contraction in extended b-metric space and prove some fixed point theorems for mappings satisfying this type contraction.

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A third-order accurate in time method for boundary layer flow problems

2020-10-29

Syed Ahmed Pasha , Yasir Nawaz , Muhammad Shoaib Arif

Fixed point theorems by altering distances between the points

1984-08-01

M. S. Khan , M. Swaleh , Salvatore Sessa

In this paper we have established some fixed point theorems in complete and compact metric spaces. In this paper we have established some fixed point theorems in complete and compact metric spaces.

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Full convergence of an approximate projection method for nonsmooth variational inequalities

2010-06-24

Yunier Bello-Cruz , Alfredo N. Iusem

Asymptotic iteration method for eigenvalue problems

2003-11-11

Hakan Çiftçi , Richard L. Hall , Nasser Saad

An asymptotic iteration method for solving second-order homogeneous linear differential equations of the form y'' = λ0(x)y' + s0(x)y is introduced, where λ0(x) ≠ 0 and s0(x) are C∞ functions. … An asymptotic iteration method for solving second-order homogeneous linear differential equations of the form y'' = λ0(x)y' + s0(x)y is introduced, where λ0(x) ≠ 0 and s0(x) are C∞ functions. Applications to Schrödinger-type problems, including some with highly singular potentials, are presented.

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Fixed and coupled fixed point theorems of omega-distance for nonlinear contraction

2013-11-08

Wasfı Shatanawi , Ariana Pitea

In this paper we utilize the notion of Ω-distance in the sense of Saadati et al. (Math. Comput. Model. 52:797-801, 2010) to construct and prove some fixed and coupled fixed … In this paper we utilize the notion of Ω-distance in the sense of Saadati et al. (Math. Comput. Model. 52:797-801, 2010) to construct and prove some fixed and coupled fixed point theorems in a complete G-metric space for a nonlinear contraction. Also, we provide an example to support our results. MSC:47H10, 54H25.

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Generalized contractions on partial metric spaces

2010-09-03

İshak Altun , Ferhan Şola Erduran , Hakan Şimşek

Fixed point results for F-contractive mappings of Hardy-Rogers-type

2014-01-01

Monica Cosentino , Pasquale Vetroa

Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present … Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.

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Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces

2013-03-12

Wasfı Shatanawi , Mihai Postolache

In this paper, we introduce the notion of a generalized -weak contraction and we prove some common fixed point results for self-mappings T and S and some fixed point results … In this paper, we introduce the notion of a generalized -weak contraction and we prove some common fixed point results for self-mappings T and S and some fixed point results for a single mapping T by using a -comparison function and a comparison function in the sense of Berinde in a partial metric space. Also, we introduce an example to support the useability of our results. MSC:47H10, 54H25.

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An approximate proximal-extragradient type method for monotone variational inequalities

2004-09-18

Bing-sheng He , Zhen-hua Yang , XiaoMing Yuan

Solving Boundary Value Problems on Networks Using Equilibrium Measures

2000-02-01

E. Bendito , Ángeles Carmona Mejías , A.M. Encinas

Banach contraction principle for cyclical mappings on partial metric spaces

2012-09-18

Thabet Abdeljawad , Jehad Alzabut , Aiman Mukheimer +1 more

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by … We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilić et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact. MSC:47H10, 54H25.

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On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation

2015-11-12

Abdon Atangana

Fixed and common fixed point theorems in partially ordered quasi-metric spaces

2016-12-15

Wasfı Shatanawi , Mohd Salmi Md Noorani , Habes Alsamir +1 more

In this paper, we prove some new fixed and common fixed point results in the framework of partially ordered quasi-metric spaces under linear and nonlinear contractions.Also we obtain some fixed … In this paper, we prove some new fixed and common fixed point results in the framework of partially ordered quasi-metric spaces under linear and nonlinear contractions.Also we obtain some fixed point results in the framework of G-metric spaces.©2016

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Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

2020-11-16

Saleh S. Redhwan , Mohammed S. ‬Abdo , Kamal Shah +4 more

A mathematical model for the spread of the COVID-19 disease based on a fractional Atangana–Baleanu operator is studied. Some fixed point theorems and generalized Gronwall inequality through the AB fractional … A mathematical model for the spread of the COVID-19 disease based on a fractional Atangana–Baleanu operator is studied. Some fixed point theorems and generalized Gronwall inequality through the AB fractional integral are applied to obtain the existence and stability results. The fractional Adams–Bashforth is used to discuss the corresponding numerical results. A numerical simulation is presented to show the behavior of the approximate solution in terms of graphs of the spread of COVID-19 in the Chinese city of Wuhan. We simulate our table for the data of Wuhan from February 15, 2020 to April 25, 2020 for 70 days. Finally, we present a debate about the followed simulation in characterizing how the transmission dynamics of infection can take place in society.

Remarks on G-metric spaces and fixed point theorems

2012-11-22

Mohamed Jleli , Bessem Samet

We discuss the introduced concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces. In particular, we show that the most obtained fixed … We discuss the introduced concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces. In particular, we show that the most obtained fixed point theorems on such spaces can be deduced immediately from fixed point theorems on metric or quasi-metric spaces. MSC:47H10, 11J83.

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On an iteration method for eigenvalue problems

2004-05-25

Francisco M. Fernández

We discuss a recently proposed asymptotic iteration method for eigenvalue problems. We analyse its rate of convergence, the use of adjustable parameters to improve it and the relationship with an … We discuss a recently proposed asymptotic iteration method for eigenvalue problems. We analyse its rate of convergence, the use of adjustable parameters to improve it and the relationship with an alternative method based on the same ideas.

A Finite Difference Method and Effective Modification of Gradient Descent Optimization Algorithm for MHD Fluid Flow over a Linearly Stretching Surface

2020-01-01

Yasir Nawaz , Muhammad Shoaib Arif , Mairaj Bibi +3 more

Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent … Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent Algorithm to solve the resulted difference equation. The flow problem is constructed using continuity, and Navier Stoke equations and these PDEs are further converted into boundary value problem by applying suitable similarity transformations. A central finite difference method is proposed that gives third-order accuracy using three grid points. The stability conditions of the present proposed method using a Gauss-Seidel iterative procedure is found using VonNeumann stability criteria and order of the finite difference method is proved by applying the Taylor series on the discretised equation. The comparison of the presently modified optimisation algorithm with the Gauss-Seidel iterative method and standard Newton's method in optimisation is also made. It can be concluded that the presently modified optimisation Algorithm takes a few iterations to converge with a small value of the parameter contained in it compared with the standard descent algorithm that may take millions of iterations to converge. The present modification of the steepest descent method converges faster than Gauss-Seidel method and standard steepest descent method, and it may also overcome the deficiency of singular hessian arise in Newton's method for some of the cases that may arise in optimisation problem(s).

A New Approach to Generalized Fractional Derivatives

2011-01-01

Udita N. Katugampola

The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^ρ\mathcal{I}^α_{a+}f\big)(x) = \frac{ρ^{1- α}}{Γ(α)} \int^x_a \frac{τ^{ρ-1} f(τ) }{(x^ρ- τ^ρ)^{1-α}}\, dτ, \] which generalizes the … The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^ρ\mathcal{I}^α_{a+}f\big)(x) = \frac{ρ^{1- α}}{Γ(α)} \int^x_a \frac{τ^{ρ-1} f(τ) }{(x^ρ- τ^ρ)^{1-α}}\, dτ, \] which generalizes the well-known Riemann-Liouville and the Hadamard fractional integrals. In this paper we present a new fractional derivative which generalizes the familiar Riemann-Liouville and the Hadamard fractional derivatives to a single form. We also obtain two representations of the generalized derivative in question. An example is given to illustrate the results.

Dirichlet problem and Green's formulas on trees

2005-11-01

Kamaleldin Abodayeh , Victor Anandam

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Generalized contractions in metric spaces endowed with a graph

2012-09-25

Cristian Chifu , Gabriela Petruşel

A very interesting approach in the theory of fixed points in some general structures was recently given by Jachymski (Proc. Amer. Math. Soc. 136:1359-1373, 2008) and Gwóźdź-Lukawska and Jachymski (J. … A very interesting approach in the theory of fixed points in some general structures was recently given by Jachymski (Proc. Amer. Math. Soc. 136:1359-1373, 2008) and Gwóźdź-Lukawska and Jachymski (J. Math. Anal. Appl. 356:453-463, 2009) by using the context of metric spaces endowed with a graph. The purpose of this article is to present some new fixed point results for graphic contractions and for Ćirić-Reich-Rus G-contractions on complete metric spaces endowed with a graph. The particular case of almost contractions is also considered. MSC:47H10, 54H25.

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Fixed points of Kannan mappings in metric spaces endowed with a graph

2012-05-01

Florin Bojor

Abstract Let (X; d) be a metric space endowed with a graph G such that the set V (G) of vertices of G coincides with X. We define the notion … Abstract Let (X; d) be a metric space endowed with a graph G such that the set V (G) of vertices of G coincides with X. We define the notion of G-Kannan maps and obtain a fixed point theorem for such mappings

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Some Asymptotic Expressions for Prolate Spheroidal Functions and for the Eigenvalues of Differential and Integral Equations of Which They Are Solutions

1972-11-01

J. des Cloizeaux , M. L. Mehta

The asymptotic behavior of the prolate spheroidal functions of order zero fn(x, c), where n is the number of zeros of the function in the interval − 1 ≤ x … The asymptotic behavior of the prolate spheroidal functions of order zero fn(x, c), where n is the number of zeros of the function in the interval − 1 ≤ x ≤ 1, is studied for large values of the parameter c and all values of n. The method used involves solving the differential equation which defines the functions by using a classical approximation. The corresponding eigenvalues χn are given by an implicit equation and the norm of the functions is calculated. The functions fn(x, c) are also solutions of an integral equation and associated with eigenvalues λn(c). Asymptotic expressions of [1 − λn(c)] are derived by using the values obtained for the norm of fn(x, c). All these results generalize and interpolate partial results obtained by Slepian and others in two special cases, namely, n finite and n ≃ c.