Q-homotopy analysis transform technique for two-dimensional fractional diffusion equation

Sarwe, D. U.; Dahraj, S.; Jatoi, M. A.; Mallah, G. Y.

doi:10.2478/jamsi-2025-0006

Abstract

In this paper, we find the solution for two-dimensional fractional diffusion equation using an efficient scheme namely, q-homotopy analysis transform method (q-HATM). To validate the competence and applicability of the proposed scheme, we consider two examples. The proposed algorithm is the joint application of the homotopy analysis method and Laplace transform (LT). For the obtained series solution, the proposed method offers ¯h-curves that illustrate convergence region. The numerical behaviour is presented to ensure the reliability and accuracy of the proposed method. Further, the nature of the achieved results is presented for a diverse order of the fractional derivative. The achieved results show that, the considered method is easy to implement and very effective to study the behaviour of nonlinear models.

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Q-homotopy analysis transform technique for two-dimensional fractional diffusion equation

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