Fareed, Aisha F.T. M. M. Elbarawy, Menna. A. Hammad, D2023-04-042023-04-042022Faculty of Engineeringhttp://repository.msa.edu.eg/xmlui/handle/123456789/5444This paper aims to present an analytical and approximation method to get the solution of the space-time fractional diffusion equation. This suggested method is based on a combination of the double and triple Laplace transforms with the Adomain decomposition method. The presented methodology is tested on illustrative examples and the results show that it is a simple, efficient, and reliable method.enMSA UniversityOctober University of Modern Sciences And ArtsDouble Laplace transform,Triple Laplace transform,Adomain decomposition method,fractional diffusion equation,Mittag-Leffler function.Article