An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory

Abstract

Abstract In this article, we suggest a numerical approach based on q‐ homotopy analysis Elzaki transform method ( q‐ HAETM) to solve fractional multidimensional diffusion equations which represents density dynamics in a material undergoing diffusion. We take the noninteger derivative in the Caputo–Fabrizio kind. The proposed method, q‐ HAETM is an advanced adaptation in q ‐HAM and Elzaki transform method which makes mathematical calculation very effective additionally more accurate. Since, in classical perturbation scheme, the scheme restricted to the small parameter whereas the q‐ HAETM is not restricted to the small parameter. By theoretical and numerical evaluation it is observed that q‐ HAETM yields an analytical solution in the form of a convergent series. By taking three examples and applying q‐ HAETM, the numerical results reveal that the suggested method is straightforward to apply and computationally very effective.