Solutions of Fractional differential equations with some modifications of Adomian Decomposition method

Abstract

In this paper, we apply the Adomian decomposition method (ADM) for solving Fractional Differential Equations (FDEs) with some modifications to the traditional method. The aim of this paper is to make ADM more efficient, rapid in convergence, and easy to use, so we will discuss two modifications. We use the reliable modification to simplify calculations. For difficulties in symbolic integration, we use a numerical implementation method. All these modifications were applied to the integer-order case, so we would apply it to FDEs. Some numerical results are given from solving these cases and comparing the solution with the ADM method.

Efficient Modified Adomian Decomposition Method for Solving Nonlinear Fractional Differential Equations

“…What is more, the powerful modifications of ADM demonstrated a rapid convergence of the series solution if compared with the standard ADM, and therefore, presented major progress. The modification of ADM has been shown to be computationally efficient in several models, which are important to researchers in applied science [20,21].…”