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

Author:

Amin Ahmed Z.1,Lopes António M.2ORCID,Hashim Ishak1

Affiliation:

1. Faculty of Science & Technology, Department of Mathematical Sciences , Universiti Kebangsaan , Bangi , Selangor , Malaysia

2. Faculty of Engineering, LAETA/INEGI , University of Porto , Porto , Portugal

Abstract

AbstractA 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

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