SOLUTION OF THE TIME- AND RIESZ SPACE-FRACTIONAL FOKKER-PLANCK EQUATION BY A STABLE GAUSSIAN RADIAL BASIS FUNCTION METHOD

L. ZEINALI, MILAD; Sepehrian, Behnam

doi:10.22034/maco.4.2.12

SOLUTION OF THE TIME- AND RIESZ SPACE-FRACTIONAL FOKKER-PLANCK EQUATION BY A STABLE GAUSSIAN RADIAL BASIS FUNCTION METHOD

Document Type : Original Article

Authors

MILAD L. ZEINALI

Behnam Sepehrian

10.22034/maco.4.2.12

Abstract

In this article the Caputo time- and Riesz space-fractional Fokker-Planck equa-
tion (TSFFPE) is solved by the stable Gaussian radial basis function (RBF) method. By a
spatial discretization and using the Riesz fractional derivative of the stable Gaussian radial
basis function interpolants computed in [23], the computations of TSFFPE reduced to a sys-
tem of fractional ODEs. A high order finite difference method is presented for this system
of ODEs, and the computations are converted to a system of linear or nonlinear algebraic
equations, in each time step. In the nonlinear case, these systems can be easily solved by
the Newton iterative method. Numerical illustrations are performed to confirm the accuracy
and efficiency of the presented method. Some comparisons are made with the results in other
literature .

Keywords

Caputo derivative

Fractional Fokker-Planck equation

Radial basis functions

Riesz derivative