Mathematics Modeling and Simulation

Fractional Differential Equations Solutions

Description

This cluster of papers focuses on the modeling, analysis, and applications of anomalous diffusion using fractional calculus, nonlinear equations, and the homotopy analysis method. It explores phenomena such as random walk, fractional derivatives, time-fractional diffusion equations, single particle tracking in biological cells, and diffusion in crowded environments.

Keywords

Anomalous Diffusion; Fractional Calculus; Nonlinear Equations; Homotopy Analysis Method; Random Walk; Fractional Derivatives; Time-Fractional Diffusion Equation; Single Particle Tracking; Biological Cells; Crowded Environments

Most Cited Works

Action Title Date Authors
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Nonlinear Functional Analysis and its Applications 1990-01-01 Eberhard Zeidler
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Solving Frontier Problems of Physics: The Decomposition Method 1994-01-01 George Adomian
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Theory and Applications of Fractional Differential Equations 2006-01-01 Anatoly A. Kilbas H. M. Srivastava Juan J. Trujillo
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The Fractional Calculus - Theory and Applications of Differentiation and Integration to Arbitrary Order 1974-01-01 Keith B. Oldham Jerome Spanier
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Introduction to Nonextensive Statistical Mechanics 2009-01-01 Constantino Tsallis
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Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers 1999-01-01 Igor Podlubný
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SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS 2006-04-19 Ji‐Huan He
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Analysis of Fractional Differential Equations 2002-01-01 Kai Diethelm Neville J. Ford
Beyond Perturbation: Introduction to the Homotopy Analysis Method 2004-09-01 Shijun Liao S. A. Sherif
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics 2004-07-22 Ralf Metzler J. Klafter
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Dual variational methods in critical point theory and applications 1973-12-01 Antonio Ambrosetti Paul H. Rabinowitz
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Variational iteration method – a kind of non-linear analytical technique: some examples 1999-07-01 Ji‐Huan He
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Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon 1981-11-09 Thomas A. Witten Leonard M. Sander
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Fractional Calculus in Bioengineering 2007-02-12 Bruce J. West
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Homotopy perturbation method: a new nonlinear analytical technique 2002-10-07 Ji‐Huan He
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Mittag–Leffler stability of fractional order nonlinear dynamic systems 2009-05-14 Yan Li YangQuan Chen Igor Podlubný
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Multidimensional nonlinear diffusion arising in population genetics 1978-10-01 D. G. Aronson Hans F. Weinberger
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking 2014-01-01 Ralf Metzler Jae‐Hyung Jeon Andrey G. Cherstvy Eli Barkai
Mean shift, mode seeking, and clustering 1995-01-01 Yizong Cheng
User’s guide to viscosity solutions of second order partial differential equations 1992-01-01 Michael G. Crandall Hitoshi Ishii Pierre-Louis Lions
A family of variable-metric methods derived by variational means 1970-01-01 Donald Goldfarb
The Geometry of Algorithms with Orthogonality Constraints 1998-01-01 Alan Edelman T. A. Arias Steven T. Smith
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Iterative Methods for the Solution of Equations. 1967-03-01 David M. Young J. F. Traub
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The ()-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics 2007-08-02 Ming L. Wang Xiangzheng Li Jinliang Zhang
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A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity 1983-06-01 Ronald L. Bagley Peter J. Torvik
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Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability 2009-08-29 Yan Li YangQuan Chen Igor Podlubný
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On certain integrals of Lipschitz-Hankel type involving products of bessel functions 1955-04-19 G. Eason B. Noble I. N. Sneddon
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Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications 1990-11-01 Jean‐Philippe Bouchaud Antoine Georges
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A new definition of fractional derivative 2014-01-16 Roshdi Khalil Mohammed Al Horani A. Yousef Mohammad Sababheh
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Chaos, fractional kinetics, and anomalous transport 2002-12-01 G. M. Zaslavsky
Recent history of fractional calculus 2010-06-01 J. A. Tenreiro Machado Virginia Kiryakova Francesco Mainardi
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Extended tanh-function method and its applications to nonlinear equations 2000-12-01 Engui Fan
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On conformable fractional calculus 2014-10-29 Thabet Abdeljawad
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A coupling method of a homotopy technique and a perturbation technique for non-linear problems 2000-01-01 Ji‐Huan He
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Meshless methods: An overview and recent developments 1996-12-01 Ted Belytschko Y. Krongauz D. Organ Mark Fleming Petr Krysl
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The topological theory of defects in ordered media 1979-07-01 N. David Mermin
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The random walk's guide to anomalous diffusion: a fractional dynamics approach 2000-12-01 Ralf Metzler J. Klafter
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Exp-function method for nonlinear wave equations 2006-05-03 Ji‐Huan He Xuhong Wu
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On the homotopy analysis method for nonlinear problems 2003-10-11 Shijun Liao
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The Fractional Order Fourier Transform and its Application to Quantum Mechanics 1980-01-01 Victor Namias
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Finite difference/spectral approximations for the time-fractional diffusion equation 2007-02-15 Yumin Lin Chuanju Xu
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Homotopy perturbation technique 1999-08-01 Ji‐Huan He
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Fractional Differential Equations - An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications 1999-01-01
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Advances in Fractional Calculus 2007-01-01 Jocelyn Sabatier Om P. Agrawal J. A. Tenreiro Machado
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A Note on the Multiplying Factors for Various χ2 Approximations 1954-07-01 M. S. Bartlett
New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model 2016-01-01 Abdon Atangana Dumitru Băleanu
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Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling 1994-01-01 Patrick Royston Douglas G. Altman
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The Analysis of Fractional Differential Equations 2010-01-01 Kai Diethelm
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Applications of Fractional Calculus in Physics 2000-03-01 R. Hilfer
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Applications of Fractional Calculus in Physics 2000-01-01 R. Hilfer

Most Recent Works

Action Title Date Authors
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Numerical solution of fractional order Bagley-Torvik equation via Hermite wavelet method 2025-05-02 Muhammad Yousaf Aman Ullah Salman Zeb Umar Farooq Kamal Shah
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On potentials and complementary potentials in one-dimensional nonlocal integral formulations 2025-05-02 Marko Čanađija Ante Skoblar
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Numerical algorithm for solving third-order Emden–Fowler type pantograph differential equations: Taylor operational matrix method 2025-05-02 Nikita Saha Randhir Singh
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Viscoelastic modeling of magnetic losses in a nanocrystalline core using fractional derivative operators 2025-05-02 Benjamin Ducharne Shengze Gao Yanhui Gao Xiao‐Jun Zhao
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Generalized Bernoulli process and fractional Poisson process 2025-05-02 Jeonghwa Lee
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Fractional differentiation method: Application to the trapping reactions in the comb-like structures with relaxation 2025-05-02 Sergey D. Traytak
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APPLICATION OF THE SOME BLAISE ABBO METHOD (SBA) FOR SOLVING THE NONLINEAR FRACTIONAL SCHRÖDINGER EQUATIONS 2025-05-02 Rashid Ali Gires Dimitri Nkaya Joseph Bonazebi Yindoula Massamba Alphonse
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Some Robust Numerical Schemes and Analysis for Solving Time Fractional Nagumo Equation 2025-05-03 Sobin Thomas S. Karthik Suresh Kumar Nadupuri
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A hybrid technique for approximating the solution of fractional order partial integro-differential equations 2025-05-02 Ahmed K. Mohsin Fajir A. Abdulkhaleq Osama H. Mohammed
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Existence and Mittag–Leffler Stability for the Solution of a Fuzzy Fractional System with Application of Laplace Transforms to Solve Fractional Differential Systems 2025-05-03 Mohammad Saeid Abolhassanifar Reza Saadati Mohammad Bagher Ghaemi Donal O’Regan
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Perturbed Caputo fractional Moreau’s sweeping process: existence, uniqueness, and numerical simulations 2025-05-05 Maria Ihsane El Bahi Zakaria Faiz Hicham Benaissa J. Vanterler da C. Sousa K. Hilal
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A New Exact Method for Bi-level Linear Fractional Problems with Multi-valued Optimal Reaction Maps 2025-05-05 Flagot Yohannes Feleke Semu Mitiku Kassa
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A non-uniform time-stepping method for time-fractional diffusion-wave equations with variable coefficients arising in fluid flow problems 2025-05-05 R. Burman Rajesh K. Pandey Sarita Kumari
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Controllability of (k,ϕ)$$ \left(k,\phi \right) $$‐Hilfer Fractional Differential Equation With Infinite Delay 2025-05-04 Ananta Thakur Javid Ali
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Derivation and Multisoliton Solutions of the High‐Order Fractional Nonlinear SchröDinger Equation for the Rossby Waves 2025-05-06 Yi Liu Huanhe Dong Baojun Zhao Jingjing Li Xiaofeng Han
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An existence results of a product type fractional functional integral equations using Petryshyn's fixed point theorem 2025-05-06 Sukanta Halder Deepmala Cemil Tunç
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Solitary wave solutions and stability analysis of the fractional Sawada-Kotera equation using the extended modified auxiliary equation mapping method 2025-05-06 Saikh Shahjahan Miah M. Ali Akbar Kamruzzaman Khan
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An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the q-Hilfer Fractional Derivative 2025-05-06 R. Vivek K. Kanagarajan D. Vivek Turki D. Alharbi E. M. Elsayed
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Sufficient Conditions for Optimal Stability in Hilfer–Hadamard Fractional Differential Equations 2025-05-06 Safoura Rezaei Aderyani Reza Saadati Donal O’Regan
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A New Numerical Technique for Solving Fractional Integro-Differential Equations in Fuzzy Space 2025-05-06 Ihab Hadi Jumhaa Hussein Jabbar Mohammed Adil K Bagheedh Uday J. Quaez
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Exploring Solitary Wave Solutions of the Generalized Integrable Kadomtsev–Petviashvili Equation via Lie Symmetry and Hirota’s Bilinear Method 2025-05-06 Beenish Maria Samreen Fehaid Salem Alshammari
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On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy 2025-05-06 Dilveen M. Ahmed Bewar A. Mahmood Ahmad Alalyani
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Soliton Solutions of an Integrable Coupled Discrete Nonlocal Nonlinear Schrdinger Equation 2025-05-06 Mengqi Lv
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On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method 2025-05-06 Faten H. Damag Amin Saif
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Relative Controllability and Finite Interval Stability of Impulsive Fractional Order Switched Delay Differential System with Nonlinear Perturbation 2025-05-06 P. K. Lakshmi Priya K. Kaliraj
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Exploring new exact solutions in the conformable time-fractional discrete coupled NLSE using a novel approach 2025-05-06 Mostafa Eslami
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Discretization of the Caputo time-fractional advection-diffusion problems with certain wavelet basis function 2025-05-07 Daniel Chinedu Iweobodo Godspower C. Abanum Ozioma Ogoegbulem Napoleon Ochonogor I.N. Njoseh
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A study on the existence of unique stable approximate solutions: fractal-fractional-based model of an energy supply–demand system 2025-05-07 Salah Boulaaras Tanzeela Kanwal İbrahim Avcı Sina Etemad Zaher Mundher Yaseen‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬
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Theoretical analysis and applications of fixed-point theorems in delay fractional differential equations 2025-05-07 Mohamed Balegh Ahmed Ghezal
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An innovative methodology in analyzing certain pendulum oscillators 2025-05-07 Galal M. Moatimid T. S. Amer A. A. Galal
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A study on solvability and an iterative method for infinite systems of fractional integro-differential equations 2025-05-07 Rahul Rahul Sukanta Halder Manochehr Kazemi Mohammad Esmael Samei
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Landmark Alternating Diffusion 2025-05-07 Sing-Yuan Yeh Hau‐Tieng Wu Ronen Talmon Mao-Pei Tsui
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Wireless Sensor Network Disease and Numerical Scheme Based on Newton Polynomial Under Fractal–Fractional Operator 2025-05-06 Jinyu Xia Qi Liu Yuxin Wang Ranran Wang Anwarud Din
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Fractal Self‐Adjoint Higher Order Boundary‐Value Problems 2025-05-07 Bilender P. Allahverdiev Hüseyin Tuna
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Enhanced Global Optimization Using a Novel Hybrid Sine Cosine-Gazelle Algorithm with Brownian Motion and Lévy Flight Mechanisms 2025-05-08 Gyan Singh Saptadeep Biswas Absalom E. Ezugwu Vladimir Šimić Uttam Kumar Bera Kashif Saleem Laith Abualigah
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Modeling and numerical simulation of Maxwell nanofluid flow with heat generation and convective heating: a combined Adomian decomposition method and Mohand transform 2025-05-08 M. M. Khader Mohamed Adel Mohammed Messaoudi
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Ulam-Hyers-Rassias stability for fractional stochastic impulsive differential equations driven by time-changed Brownian motion followed by credit risk modeling 2025-05-08 Dimplekumar Chalishajar Dhanalakshmi Kasinathan Ravikumar Kasinathan Ramkumar Kasinathan
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An iterative scheme for nonlinear collision-induced breakage equation and convergence analysis 2025-05-08 Sanjiv Kumar Bariwal Rajesh Kumar
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Analysis of Iterative Method for Impulsive Neutral Functional Integro-Differential Equation Using Degree Theory 2025-05-08
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Probing intrinsic noise correlation time in non-Markovian diffusive systems 2025-05-08 Ming-Gen Li Xiao Dong He-Chuan Liu Jing-Dong Bao Peng-Cheng Li L.T. Fan
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Homotopy Perturbation <i>ρ</i>-Laplace Transform Approach for Numerical Simulation of Fractional Navier-Stokes Equations 2025-05-09 Hamza Mihoubi Awatif Muflih Alqahtani Yacine Arioua Brahim Bouderah Tahar Tayebi
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Fractional triple-phase lag theory with non-singular kernels: analyzing the thermo-viscoelastic behavior of living skin tissue with bioheat transfer 2025-05-09 Ahmed E. Abouelregal Mohamed Salem Yazeed Alhassan Hamid M. Sedighi Mohammad Kordi
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Numerical Solutions of Time-Fractional N-W-S and Burger’s Equations Using the Tarig Projected Differential Transform Method (TPDTM) 2025-05-09 K Athira D Narasimhulu P. S. Brahmanandam
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Practical stabilization for a class of tempered fractional‐order nonlinear fuzzy systems 2025-05-09 Hafedh Rguigui Moncef Elghribi
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Analytical solutions of the time-fractional symmetric regularized long wave equation using the $$\phi ^{6}$$ model expansion method 2025-05-09 Khaled Aldwoah Nidal H. E. Eljaneid Bassam A. Younis Mohammed Alsharafi Osman Osman Blgys Muflh
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Solutions behavior of mechanical oscillator equations with impulsive effects under Power Caputo fractional operator and its symmetric cases 2025-05-09 Hicham Saber Mohammed A. ‬Almalahi Mohamed Bouye Khaled Aldwoah Abdelkader Moumen Blgys Muflh
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Fractional analysis of time-fractional Emden-Fowler problem in the fluid flow through a porous medium 2025-05-09 Muhammad Nadeem Yabin Shao M. Riaz Khan Azeem Hafiz P A Ebraheem Alzahrani
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Approximate Solution of the Nonlinear Buckmaster Partial Differential Equation using Exponential Fourth-order Differentiable Functions 2025-05-09 Usman Mohammed Yusuf Moses Anayo Mbah Collins E. Akpan Abubakar Abdulkarim María Jesús Teixidor de Otto Aminu Buhari Godwin Ma'aji Philip Nwanosike
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Modeling the Media Impact on the Medication Behavior of Drug-Sensitive Patients in Two-Strain Tuberculosis Transmission and a Case Study 2025-05-09 Jun Zhang Yuhang Ma Y Takeuchi Yueping Dong Zhihang Peng
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Application of the Tanh–Coth and HSI methods in deriving exact analytical solutions for the STFKS equation 2025-05-09 Abaker A. Hassaballa Elzain A. E. Gumma Ahmed M. A. Adam Omer M. A. Hamed Ali Satty Mohyaldein Salih Faroug A. Abdalla Zakariya M. S. Mohammed