A higher order numerical scheme for solving fractional Bagley-Torvik equation

In this paper, we develop a higher order numerical method for the fractional Bagley-Torvik equation. The main tools used include a new fourth-order approximation for the fractional derivative based on the weighted shifted Grunwald-Letnikov difference operator and a discrete cubic spline approach. We show that the theoretical convergence order improves those of previous work. Five examples are further presented to illustrate the efficiency of our method and to compare with other methods in the literature.