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An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory
Author(s) -
Singh Jagdev,
Kumar Devendra,
Purohit Sunil Dutt,
Mishra Aditya Mani,
Bohra Mahesh
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22601
Subject(s) - mathematics , fractional calculus , convergent series , numerical analysis , exponential function , scheme (mathematics) , mathematical analysis , power series
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.