Browsing by Author "Shakoor Muhammad"
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Item Application of asymptotic homotopy perturbation method to fractional order partial differential equation(MDPI, 2021) Haji Gul; Sajjad Ali; Kamal Shah; Shakoor Muhammad; Thanin Sitthiwirattham; Saowaluck Chasreechai; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this article, we introduce a new algorithm-based scheme titled asymptotic homotopy perturbation method (AHPM) for simulation purposes of non-linear and linear differential equations of non-integer and integer orders. AHPM is extended for numerical treatment to the approximate solution of one of the important fractional-order two-dimensional Helmholtz equations and some of its cases . For probation and illustrative purposes, we have compared the AHPM solutions to the solutions from another existing method as well as the exact solutions of the considered problems. Moreover, it is observed that the symmetry or asymmetry of the solution of considered problems is invariant under the homotopy definition. Error estimates for solutions are also provided. The approximate solutions of AHPM are tabulated and plotted, which indicates that AHPM is effective and explicit. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.