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

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.