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

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 t...

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Autores principales:	Haji Gul, Sajjad Ali, Kamal Shah, Shakoor Muhammad, Thanin Sitthiwirattham, Saowaluck Chasreechai
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	fractional order partial differential equation caputo derivative asymptotic homotopy perturbation method AHPM Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/608022df54de474789c49860c7d06386
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spelling	oai:doaj.org-article:608022df54de474789c49860c7d063862021-11-25T19:07:39ZApplication of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation10.3390/sym131122152073-8994https://doaj.org/article/608022df54de474789c49860c7d063862021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2215https://doaj.org/toc/2073-8994In 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.Haji GulSajjad AliKamal ShahShakoor MuhammadThanin SitthiwiratthamSaowaluck ChasreechaiMDPI AGarticlefractional order partial differential equationcaputo derivativeasymptotic homotopy perturbation methodAHPMMathematicsQA1-939ENSymmetry, Vol 13, Iss 2215, p 2215 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fractional order partial differential equation caputo derivative asymptotic homotopy perturbation method AHPM Mathematics QA1-939
spellingShingle	fractional order partial differential equation caputo derivative asymptotic homotopy perturbation method AHPM Mathematics QA1-939 Haji Gul Sajjad Ali Kamal Shah Shakoor Muhammad Thanin Sitthiwirattham Saowaluck Chasreechai Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation
description	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.
format	article
author	Haji Gul Sajjad Ali Kamal Shah Shakoor Muhammad Thanin Sitthiwirattham Saowaluck Chasreechai
author_facet	Haji Gul Sajjad Ali Kamal Shah Shakoor Muhammad Thanin Sitthiwirattham Saowaluck Chasreechai
author_sort	Haji Gul
title	Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation
title_short	Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation
title_full	Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation
title_fullStr	Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation
title_full_unstemmed	Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation
title_sort	application of asymptotic homotopy perturbation method to fractional order partial differential equation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/608022df54de474789c49860c7d06386
work_keys_str_mv	AT hajigul applicationofasymptotichomotopyperturbationmethodtofractionalorderpartialdifferentialequation AT sajjadali applicationofasymptotichomotopyperturbationmethodtofractionalorderpartialdifferentialequation AT kamalshah applicationofasymptotichomotopyperturbationmethodtofractionalorderpartialdifferentialequation AT shakoormuhammad applicationofasymptotichomotopyperturbationmethodtofractionalorderpartialdifferentialequation AT thaninsitthiwirattham applicationofasymptotichomotopyperturbationmethodtofractionalorderpartialdifferentialequation AT saowaluckchasreechai applicationofasymptotichomotopyperturbationmethodtofractionalorderpartialdifferentialequation
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Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation

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