Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis

Tedjani A., Amin A. Z. M. A., Abdel-Aty A., Abdelkawy M., Mahmoud M.

AIMS Mathematics, vol.9, no.4, pp.7973-8000, 2024 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.3934/math.2024388
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.7973-8000
  • Keywords: Caputo fractional derivative, convergence analysis, fractional Fredholm integro-differential equation, Legendre-Gauss-Lobatto, spectral method
  • Istanbul Gelisim University Affiliated: No

Abstract

The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main idea is to use Caputo derivatives and Legendre-Gauss interpolation for nonlinear FFIDEs. A rigorous convergence analysis is provided and confirmed by numerical tests. In addition, we provide some numerical test cases to demonstrate that the approach can preserve the non-smooth solution of the underlying problem.