A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley-Torvik differential equation

Amin A. Z. M. A., Lopes A. M., Hashim I.

International Journal of Nonlinear Sciences and Numerical Simulation, vol.24, no.5, pp.1613-1630, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.1515/ijnsns-2021-0395
  • Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1613-1630
  • Keywords: Caputo fractional derivative of variable order, fractional Bagley-Torvik differential equation, shifted Chebyshev polynomials, spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

A numerical approach based on the shifted Chebyshev-Gauss collocation method is proposed for solving the non-linear variable-order fractional Bagley-Torvik differential equation (VO-FBTE), subject to initial and boundary conditions. The shifted fractional Chebyshev-Gauss collocation points are used as interpolation nodes, and the solution of the VO-FBTE is approximated by a truncated series of the shifted Chebyshev polynomials. The residuals are calculated at the shifted fractional Chebyshev-Gauss quadrature points. The original VO-FBTE is converted into a system of algebraic equations. The accuracy of the proposed scheme is confirmed with a set of numerical examples, and the results are compared with those obtained by other methods.