An efficient method for nonlinear fractional differential equations: combination of the Adomian decomposition method and spectral method

In this paper, a novel iterative method is employed to give approximate solutions of nonlinear differential equations of fractional order. This approach is based on combination of two different methods which are the Adomian decomposition method (ADM) and the spectral Adomian decomposition method (SADM). The method reduces the nonlinear differential equations to systems of linear algebraic equations and then the resulting systems are solved by a numerical method. Investigating some illustrations, we demonstrate that the obtained numerical results are in a very good agreement with the exact solutions.