Numerical solution of fractional Bagley–Torvik equations using Lucas polynomials

The aim of this article is to present a new method based on Lucas poly-nomials and residual error function for a numerical solution of fractional Bagley–Torvik equations. Here, the approximate solution is expanded as a linear combination of Lucas polynomials, and by using the collocation method, the original problem is reduced to a system of linear equations. So, the approximate solution to the problem could be found by solving this system. Then, by using the residual error function and approximating the error function by utilizing the same approach, we achieve more accurate results. In addition, the convergence analysis of the method is investi-gated. Numerical examples demonstrate the validity and applicability of the method.