Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

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

Fractal and Fractional, vol.6, no.1, 2022 (SCI-Expanded, SSCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.3390/fractalfract6010019
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, INSPEC, Directory of Open Access Journals
  • Keywords: Fractional-order shifted Jacobi polynomial, Riemann–Liouville fractional derivative, Riemann–Liouville fractional integral, Variable-order fractional integro-differential equation
  • Open Archive Collection: AVESIS Open Access Collection
  • Istanbul Gelisim University Affiliated: No

Abstract

We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.