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

Botros, Monica; Ziada, E. A.A.; El-Kalla, I. L.

doi:10.21608/dusj.2023.291073

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

Document Type : Original research papers

Authors

¹ Department of Basic science, Faculty of Engineering, Delta University for science and technology, Mansoura. Egypt,

² Nile Higher Institute for Engineering and Technology, Mansoura, Egypt

³ Department of Mathematics and Physics, Faculty of Engineering, Mansoura University, Mansoura, Egypt.

10.21608/dusj.2023.291073

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.

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