Numerical solution of the distributed-order fractional Bagley-Torvik equation

In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation. This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function. Using the composite Boole 02BC &#xs rule the distributed-order Bagley-Torvik equation is approximated by a multi-term time-fractional equation, which is then solved by the Grunwald-Letnikov method ( GLM ) and the fractional differential transform method ( FDTM ). Finally, we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.