A SPACE-TIME SPECTRAL COLLOCATION METHOD FOR SOLVING THE VARIABLE-ORDER FRACTIONAL FOKKER-PLANCK EQUATION

Amin A. Z. M. A., Lopes A. M., Hashim I.

Journal of Applied Analysis and Computation, vol.13, no.2, pp.969-985, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.11948/20220254
  • Journal Name: Journal of Applied Analysis and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.969-985
  • Keywords: Caputo fractional derivative of variable or-der, Fractional calculus, fractional Fokker-Planck equation, spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

A numerical approach for solving the variable-order fractional Fokker-Planck equation (VO-FFPE) is proposed. The computational scheme is based on the shifted Legendre Gauss-Lobatto and the shifted Chebyshev Gauss-Radau collocation methods. The VO-FFPE is written as a truncated series of shifted Legendre and shifted Chebyshev polynomials for space and time variables, respectively. The residuals of the VO-FFPE at the shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau quadrature points are estimated. The original problem is converted into a system of algebraic equations that can be solved easily. Several examples are presented to demonstrate the efficacy of the technique.