Fractal and Fractional (Dec 2021)

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

  • Mohamed A. Abdelkawy,
  • Ahmed Z. M. Amin,
  • António M. Lopes,
  • Ishak Hashim,
  • Mohammed M. Babatin

DOI
https://doi.org/10.3390/fractalfract6010019
Journal volume & issue
Vol. 6, no. 1
p. 19

Abstract

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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.

Keywords