Spectral technique for solving variable-order fractional Volterra integro-differential equations

Doha E., Abdelkawy M., Amin A. Z. M. A., Baleanu D.

Numerical Methods for Partial Differential Equations, vol.34, no.5, pp.1659-1677, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1002/num.22233
  • Journal Name: Numerical Methods for Partial Differential Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1659-1677
  • Keywords: fractional calculus, Integro-differential equation, Riemann-Liouville fractional of variable order, shifted Legendre-Gauss-Lobatto quadrature, spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

This article, presented a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method which is introduced for solving variable-order fractional Volterra integro-differential equation (VO-FVIDEs) subject to initial or nonlocal conditions. Based on shifted Legendre Gauss-Lobatto (SL-GL) quadrature, we treat with integral term in the aforementioned problems. Via the current approach, we convert such problem into a system of algebraic equations. After that we obtain the spectral solution directly for the proposed problem. The high accuracy of the method was proved by several illustrative examples.