On spectral methods for solving variable-order fractional integro-differential equations

Doha E., Abdelkawy M., Amin A. Z. M. A., Lopes A. M.

Computational and Applied Mathematics, vol.37, no.3, pp.3937-3950, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1007/s40314-017-0551-9
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3937-3950
  • Keywords: Fractional calculus, Shifted Jacobi–Gauss-quadrature, Spectral collocation method, Variable-order fractional operator
  • Istanbul Gelisim University Affiliated: No

Abstract

This paper applies the shifted Jacobi–Gauss collocation (SJ–G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann–Liouville fractional derivative, Dν(x), and integral, Iν(x), of variable order are combined, and the SJ–G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods.