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The transport dynamics in complex systems governing by anomalous diffusion modelled with Riesz fractional partial differential equations
Author(s) -
Ray Santanu Saha
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4084
Subject(s) - mathematics , fractional calculus , fokker–planck equation , operator (biology) , mathematical analysis , anomalous diffusion , finite difference method , partial differential equation , domain (mathematical analysis) , space (punctuation) , riesz potential , finite difference , biochemistry , chemistry , knowledge management , linguistics , innovation diffusion , philosophy , repressor , computer science , transcription factor , gene
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.