General one-dimensional model of the time-fractional diffusion-wave equation in various geometries

Ján Terpák

Type: Article

Publication Date: 2023-03-20

Citations: 1

DOI: https://doi.org/10.1007/s13540-023-00138-3

Abstract

Abstract This paper deals with the analysis of the time-fractional diffusion-wave equation as one-dimensional problem in a large plane wall, long cylinder, and sphere. The result of the analysis is the proposal of one general mathematical model that describes various geometries and different processes. Finite difference method for solving the time-fractional diffusion-wave equation using Grünwald-Letnikov definition for homogeneous or inhomogeneous material and for homogeneous or inhomogeneous boundary conditions is described. Dirichlet, Neumann and Robin boundary conditions are considered. Implementation of numerical methods for explicit, implicit, and Crank-Nicolson scheme were realised in MATLAB. Finally, illustrative examples of simulations using the developed toolbox are presented.

Locations

Fractional Calculus and Applied Analysis - View - PDF

Similar Works

Action	Title	Year	Authors
+	Fractional diffusion-wave problem in cylindrical coordinates	2008	Necati Özdemir Derya Karadeniz
+	Numerical method for the fractional order diffusion-wave equation	2011	Liping Wen
+	Analysis of an axis-symmetric fractional diffusion-wave problem	2009	Necati Özdemir Om P. Agrawal Derya Karadeniz Beyza Billur İskender
+	Compact implicit difference approximation for time-fractional diffusion-wave equation	2021	Umair Ali Azhar Iqbal Muhammad Umer Sohail Farah Aini Abdullah Zohaib Khan
+	Mixed finite-element method for multi-term time-fractional diffusion and diffusion-wave equations	2017	Meng Li Chengming Huang Wanyuan Ming
+	Radial basis functions and FDM for solving fractional diffusion-wave equation	2014	Z. Avazzadeh Vahid Reza Hosseini W Chen
+	Numerical simulation of higher-order diffusion-wave equations of variable coefficients using the meshless spectral method	2020	Manzoor Hussain Sirajul Haq
+ PDF Chat	A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms	2019	Nauman Khalid Muhammad Abbas Muhammad Kashif Iqbal Dumitru Băleanu
+	Numerical Method for Simulation of Fractional Diffusion-Wave Equation	2018	Seshu Kumar Damarla Madhusree Kundu
+	Numerical solution for time fractional-order diffusion-wave equation using explicit finite difference method in web service form	2017	Ján Terpák Pavel Horovčák Matej Lukac
+	Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain	2012	Hui Jiang F. Liu Ian Turner Kevin Burrage
+ PDF Chat	Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative	2023	Ibrahim Elkott M. S. Abdel Latif I. L. El‐Kalla A. H. Abdel Kader
+	Non-central-symmetric solution to time-fractional diffusion-wave equation in a sphere under Dirichlet boundary condition	2012	Yuriy Povstenko
+	Initial value problem for the two-dimensional time-fractional generalized convection-reaction-diffusion-wave equation: Invariant subspaces and exact solutions	2021	P. Prakash K. S. Priyendhu K. M. Anjitha
+	A numerical combined algorithm in cubic B-spline method and finite difference technique for the time-fractional nonlinear diffusion wave equation with reaction and damping terms	2022	Omar Abu Arqub Soumia Tayebi Dumitru Băleanu M.S. Osman Waleed S. Mahmoud Hamed Alsulami
+	Solving fractional diffusion and fractional diffusion-wave equations by Petrov-Galerkin finite element method	2014	Alaattin Esen Yusuf Uçar Nuri Murat Yağmurlu Orkun Taşbozan
+	The time discontinuous space-time finite element method for fractional diffusion-wave equation	2019	Yunying Zheng Zhengang Zhao
+	A new spline technique for the time fractional diffusion-wave equation	2023	Suruchi Singh Swarn Singh Anu G. Aggarwal
+	Separation of variables method for fractional diffusion-wave equation with initial-boundary value problem in three dimensions	2007	Fawang Liu
+	Numerical Analysis for the Variable Order Time Fractional Diffusion-Wave Equation	2020	Fupeng Tian

Works That Cite This (1)

Action	Title	Year	Authors
+ PDF Chat	Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition	2023	Vetlugin Dzhabrailovich Beybalaev А. А. Аливердиев Jordan Hristov

Works Cited by This (33)

Action	Title	Year	Authors
+ PDF Chat	Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation	2005	F. Liu Shigang Shen Vo Anh Ian Turner
+	An Introduction to the Fractional Calculus and Fractional Differential Equations	1993	Kenneth S. Miller Bertram Ross
+	A brief history and exposition of the fundamental theory of fractional calculus	1975	Bertram Ross
+ PDF Chat	Matrix approach to discrete fractional calculus II: Partial fractional differential equations	2009	Igor Podlubný Aleksei V. Chechkin Tomáš Škovránek YangQuan Chen Blas M. Vinagre
+	Heat conduction modeling by using fractional-order derivatives	2015	Monika Žecová Ján Terpák
+	Implicit difference approximation for the time fractional diffusion equation	2006	Peixian Zhuang F. Liu
+	A numerical scheme for initial compliance and creep response of a system	2009	Om P. Agrawal
+ PDF Chat	Approximation of the Lévy–Feller advection–dispersion process by random walk and finite difference method	2006	Q. Liu F. Liu Ian Turner Vo Anh
+	Least squares finite-element solution of a fractional order two-point boundary value problem	2004	George J. Fix J.P. Roof
+	An approximate method for numerical solution of fractional differential equations	2006	Pankaj Kumar Om P. Agrawal