Analytical Solution For Time-Fractional Diffusion Equation By Aboodh Decomposition Method

Abstract

In this paper, the derivation of exact solutions of time-fractional heat diffusion equations by employing the new integral transform, the Aboodh transform coupled to the Adomian decomposition method is proposed. The coupling is based on the Caputo fractional derivative definition solely chosen owing to its flexibility. The proposed method is in fact, very reliable as it gives exact solutions in little iteration without requiring either of discretization, perturbation or linearization among others. Some test examples are given with their graphical illustration.