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Article

Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation

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Department of Mathematics, Abdulwali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan
2
Department of Mathematics, Shaheed Benazir Bhutto University Sheringal Dir (Upper), Sheringal Dir (Upper) 18050, Khyber Pakhtunkhwa, Pakistan
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Department of Mathematics, University of Malakand, Chakadara Dir (Lower), Lower Dir 18800, Khyber Pakhtunkhwa, Pakistan
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Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
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Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
*
Author to whom correspondence should be addressed.
Academic Editors: Clemente Cesarano and Juan Luis García Guirao
Symmetry 2021, 13(11), 2215; https://doi.org/10.3390/sym13112215
Received: 2 October 2021 / Revised: 3 November 2021 / Accepted: 15 November 2021 / Published: 19 November 2021
In 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. View Full-Text
Keywords: fractional order partial differential equation; caputo derivative; asymptotic homotopy perturbation method; AHPM fractional order partial differential equation; caputo derivative; asymptotic homotopy perturbation method; AHPM
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MDPI and ACS Style

Gul, H.; Ali, S.; Shah, K.; Muhammad, S.; Sitthiwirattham, T.; Chasreechai, S. Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation. Symmetry 2021, 13, 2215. https://doi.org/10.3390/sym13112215

AMA Style

Gul H, Ali S, Shah K, Muhammad S, Sitthiwirattham T, Chasreechai S. Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation. Symmetry. 2021; 13(11):2215. https://doi.org/10.3390/sym13112215

Chicago/Turabian Style

Gul, Haji, Sajjad Ali, Kamal Shah, Shakoor Muhammad, Thanin Sitthiwirattham, and Saowaluck Chasreechai. 2021. "Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation" Symmetry 13, no. 11: 2215. https://doi.org/10.3390/sym13112215

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