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research-article

The Transport Dynamics Induced by Riesz Potential in modelling Fractional Reaction-Diffusion-Mechanics System

[+] Author and Article Information
Santanu Saha Ray

National Institute of Technology, Department of Mathematics, Rourkela-769008, India
saharays@nitrkl.ac.in
santanusaharay@yahoo.com

1Corresponding author.

ASME doi:10.1115/1.4037418 History: Received May 17, 2017; Revised July 11, 2017

Abstract

This paper comprises of a second-order finite difference method with implicit scheme to the Riesz fractional reaction-diffusion equation (RFRDE) by utilizing the fractional centered difference to approximate the Riesz fractional derivative, and consequently we obtain an implicit scheme which is proved to be convergent and unconditionally stable. Also a novel analytical approximate method has been dealt with namely optimal homotopy asymptotic method (OHAM) to find the solution of Riesz fractional reaction-diffusion equation. The numerical solutions of RFRDE obtained by proposed implicit finite difference method have been compared with the solutions of OHAM and also with the exact solutions. The comparative study between the solutions establishes the accuracy and efficiency of the techniques in solving Riesz fractional reaction-diffusion equation. The proposed OHAM renders a simple and robust way for the controllability and adjustment of the convergence region and is applicable to solve Riesz fractional reaction-diffusion equation.

Copyright (c) 2017 by ASME
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