Numerical Solution of Fraction Bagley–Torvik Boundary Value Problem Based on Chebyshev Collocation Method

Abstract

The Bagley–Torvik boundary value problems are used in several branches of applied mathematics and mechanics. Therefore, there is a necessity of a numerical scheme for the solution of these problems. In this paper, we propose an efficient Chebyshev collocation scheme to solve a special kind of two-point fractional Bagley–Torvik equation considering the fractional derivative in the Caputo sense. The given problem is successfully reduced into the system of algebraic equations with a particular choice of collocation points. The error analysis and convergence criteria of the present scheme are also discussed. We get good results in the sense that just a few terms of basis functions (SCPFK) are required. The given scheme is simple and powerful in use to solve such problems since boundary conditions are taken into account automatically. The efficiency and accuracy of the present scheme are examined through numerical examples and comparison with existing methods.