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Behnam Sepehrian

Behnam Sepehrian

Academic rank: Assistant Professor
ORCID: https://orcid.org/0000-0001-5524-8810
Education: PhD.
ScopusId: 6508297265
HIndex:
Faculty: Science
Address: Arak University
Phone:

Research

Title
Solution of the Liouville-Caputo time- and Riesz space-fractional Fokker-Planck equation via radial basis functions
Type
JournalPaper
Keywords
Collocation method; fractional Fokker–Planck equation; Liouville–Caputo derivative; radial basis functions; Riemann–Liouville derivative.
Year
2022
Journal asian-european journal of mathematics
DOI
Researchers Behnam Sepehrian ، zahra shamohammadi

Abstract

In this paper, radial basis functions (RBFs) method is proposed for numerical solution of the Liouville–Caputo time- and Riesz space-fractional Fokker–Planck equation with a nonlinear source term. The left-sided and the right-sided Riemann–Liouville fractional derivatives of RBFs are computed and utilized to approximate the spatial fractional derivatives of the unknown function. Also, the time-fractional derivative is discretized by the high order formulas introduced in [J. X. Cao, C. P. Li and Y. Q. Chen, High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II), Fract. Calculus Appl. Anal. 18(3) (2015) 735–761]. In each time step, via a collocation method, the computations of fractional Fokker–Planck equation are reduced to a linear or nonlinear system of algebraic equations. Several numerical examples are included to demonstrate the applicability, accuracy and stability of the method. Some comparisons are made with the existing results.