A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley-Torvik differential equation
International Journal of Nonlinear Sciences and Numerical Simulation, vol.24, no.5, pp.1613-1630, 2023 (SCI-Expanded, Scopus)
- 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.