The transport dynamics in complex systems governing by anomalous diffusion modelled with Riesz fractional partial differential equations. (2nd August 2016)

• Record Type: Journal Article
• Authors: Ray, Santanu Saha
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 5(2017)
• Page Start: 1637
• Page End: 1648
• Publication Date: 2016-08-02
• Subjects: Riesz space fractional derivative -- shifted Grünwald approximation -- fractional centred difference -- fractional Fokker–Planck equation -- left Riemann–Liouville derivative -- right Riemann–Liouville derivative; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4084
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, numerical solutions of fractional Fokker–Planck equations with Riesz space fractional derivatives have been developed. Here, the fractional Fokker–Planck equations have been considered in a finite domain. In order to deal with the Riesz fractional derivative operator, shifted Grünwald approximation and fractional centred difference approaches have been used. The explicit finite difference method and Crank–Nicolson implicit method have been applied to obtain the numerical solutions of fractional diffusion equation and fractional Fokker–Planck equations, respectively. Numerical results are presented to demonstrate the accuracy and effectiveness of the proposed numerical solution techniques. Copyright © 2016 John Wiley & Sons, Ltd.