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A numerical algorithm for the space and time fractional Fokker-Planck equation. (English) Zbl 1357.65203
Summary: Purpose
– The purpose of this paper is to present an algorithm based on operational Tau method (OTM) for solving fractional Fokker-Planck equation (FFPE) with space- and time-fractional derivatives. Fokker-Planck equation with positive integer order is also considered.
Design/methodology/approach
– The proposed algorithm converts the desired FFPE to a set of algebraic equations using orthogonal polynomials as basis functions. The paper states some concepts, properties and advantages of proposed algorithm and its applications for solving FFPE.
Findings
– Some illustrative numerical experiments including linear and nonlinear FFPE are given and some comparisons are made between OTM and variational iteration method, Adomian decomposition method and homotpy perturbation method.
Originality/value
– Results demonstrate some capabilities of the proposed algorithm such as the simplicity, the accuracy and the convergency. Also, this is the first presentation of this algorithm for FFPE.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q84 Fokker-Planck equations
35R11 Fractional partial differential equations
Software:
FODE
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Full Text: DOI
References:
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