Numerical Solution of Space-Time-Fractional Reaction-Diffusion Equations via the Caputo and Riesz Derivatives

2019 ◽  
pp. 161-188 ◽  
Author(s):  
Kolade M. Owolabi ◽  
Hemen Dutta
Keyword(s):  
Numerical Solution ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Fractional Reaction

A Green’s function approach for the numerical solution of a class of fractional reaction–diffusion equations

2016 ◽  
Vol 121 ◽  
pp. 133-145 ◽  
Author(s):  
Eliseo Hernandez-Martinez ◽  
Francisco Valdés-Parada ◽  
Jose Alvarez-Ramirez ◽  
Hector Puebla ◽  
Epifanio Morales-Zarate
Keyword(s):  
Green’S Function ◽  
Numerical Solution ◽  
Green's Function ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Function Approach ◽  
Diffusion Equations ◽  
Fractional Reaction

Analytical Solution of Linear and Non-Linear Space-Time Fractional Reaction-Diffusion Equations

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Sefa A Sezer
Keyword(s):  
Analytical Solution ◽  
Linear Space ◽  
Homotopy Perturbation Method ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Fractional Reaction

In this study, we present the homotopy perturbation method (HPM) for finding the analytical solution of linear and non-linear space-time fractional reaction-diffusion equations (STFRDE) on a finite domain. These equations are obtained from standard reaction-diffusion equations by replacing a second-order space deri-vative by a fractional derivative of order and a first-order time derivative by a fractional derivative of order. Some examples are given. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to linear and non-linear space-time fractional reaction-diffusion equations.

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