A space–time spectral approximation for solving nonlinear variable-order fractional sine and Klein–Gordon differential equations

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

Computational and Applied Mathematics, vol.37, no.5, pp.6212-6229, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1007/s40314-018-0695-2
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.6212-6229
  • Keywords: Caputo fractional derivative of variable order, Fractional calculus, Fractional sine and Klein–Gordon differential equation, Spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

In this paper, we propose an efficient spectral numerical method for solving sine and Klein–Gordon nonlinear variable-order fractional differential equations with the initial and Dirichlet boundary conditions. The approach is based on the shifted Legendre–Gauss and Chebyshev–Gauss collocation methods. The Caputo fractional derivative of variable order is adopted, and the original problems are reduced to systems of algebraic equations. The validity and effectiveness of the method is demonstrated by means of several numerical examples.