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, cilt.13, sa.2, ss.969-985, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.11948/20220254
  • Dergi Adı: Journal of Applied Analysis and Computation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.969-985
  • Anahtar Kelimeler: Caputo fractional derivative of variable or-der, Fractional calculus, fractional Fokker-Planck equation, spectral collocation method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

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.