Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations

We are concerned here with a multi-term nonlinear fractional differential equation (FDE). Two methods are used to solve this type of equations. The first is an analytical method; Adomian decomposition method (ADM). Convergence analysis of this method is discussed. This analysis is used to estimate the maximum absolute truncated error of Adomian's series solution. The second method is a proposed numerical method (PNM). A comparison between the results of the two methods is given. One of the important applications of these equations is Bagley–Torvik equation.