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

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.