Numerical Solution of Two Dimensional Time-Space Fractional Fokker Planck Equation With Variable Coefficients

Elsayed I. Mahmoud and Viktor N. Orlov
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Elsayed I. Mahmoud: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
Viktor N. Orlov: Department of Applied Math, Moscow State University of Civil Engineering, Yaroslavskoe Shosse, 26, 129337 Moscow, Russia

Mathematics, 2021, vol. 9, issue 11, 1-12

Abstract: This paper presents a practical numerical method, an implicit finite-difference scheme for solving a two-dimensional time-space fractional Fokker–Planck equation with space–time depending on variable coefficients and source term, which represents a model of a Brownian particle in a periodic potential. The Caputo derivative and the Riemann–Liouville derivative are considered in the temporal and spatial directions, respectively. The Riemann–Liouville derivative is approximated by the standard Grünwald approximation and the shifted Grünwald approximation. The stability and convergence of the numerical scheme are discussed. Finally, we provide a numerical example to test the theoretical analysis.

Keywords: two-dimensional time–space fractional Fokker–Planck equation; standard and shifted Grünwald approximation; Riemann–Liouville fractional derivative; Caputo fractional derivative; implicit finite difference scheme; stability and convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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