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

Author

Listed:
  • Elsayed I. Mahmoud

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
    Nikolskii Mathematical Institute, Peoples Friendship University of Russia, 117198 Moscow, Russia)

  • Viktor N. Orlov

    (Department of Applied Math, Moscow State University of Civil Engineering, Yaroslavskoe Shosse, 26, 129337 Moscow, Russia)

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.

Suggested Citation

  • Elsayed I. Mahmoud & Viktor N. Orlov, 2021. "Numerical Solution of Two Dimensional Time-Space Fractional Fokker Planck Equation With Variable Coefficients," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1260-:d:566099
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    Cited by:

    1. Victor N. Orlov & Asmaa M. Elsayed & Elsayed I. Mahmoud, 2022. "Two Linearized Schemes for One-Dimensional Time and Space Fractional Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-16, October.

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