On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method

In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required so...

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Autores principales:	Muhammad Sinan, Kamal Shah, Zareen A. Khan, Qasem Al-Mdallal, Fathalla Rihan
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ca9d89d43ce54851ba80b5d4ded8a4ae
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spelling	oai:doaj.org-article:ca9d89d43ce54851ba80b5d4ded8a4ae2021-11-15T01:19:25ZOn Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method2314-478510.1155/2021/6045722https://doaj.org/article/ca9d89d43ce54851ba80b5d4ded8a4ae2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/6045722https://doaj.org/toc/2314-4785In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required solution. We obtain the solution in the form of infinite series. We next triggered different parametric effects (such as x, t, and so on) on the structure of the solitary wave propagation, demonstrating that the breadth and amplitude of the solitary wave potential may alter when these parameters are changed. We have demonstrated that He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation through our calculations and simulations. We may apply our method to an additional complicated problem, particularly on the applied side, such as astrophysics, plasma physics, and quantum mechanics, to perform complex theoretical computation. Graphical presentation of few terms approximate solutions are given at different fractional orders.Muhammad SinanKamal ShahZareen A. KhanQasem Al-MdallalFathalla RihanHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Muhammad Sinan Kamal Shah Zareen A. Khan Qasem Al-Mdallal Fathalla Rihan On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
description	In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required solution. We obtain the solution in the form of infinite series. We next triggered different parametric effects (such as x, t, and so on) on the structure of the solitary wave propagation, demonstrating that the breadth and amplitude of the solitary wave potential may alter when these parameters are changed. We have demonstrated that He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation through our calculations and simulations. We may apply our method to an additional complicated problem, particularly on the applied side, such as astrophysics, plasma physics, and quantum mechanics, to perform complex theoretical computation. Graphical presentation of few terms approximate solutions are given at different fractional orders.
format	article
author	Muhammad Sinan Kamal Shah Zareen A. Khan Qasem Al-Mdallal Fathalla Rihan
author_facet	Muhammad Sinan Kamal Shah Zareen A. Khan Qasem Al-Mdallal Fathalla Rihan
author_sort	Muhammad Sinan
title	On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
title_short	On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
title_full	On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
title_fullStr	On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
title_full_unstemmed	On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
title_sort	on semianalytical study of fractional-order kawahara partial differential equation with the homotopy perturbation method
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/ca9d89d43ce54851ba80b5d4ded8a4ae
work_keys_str_mv	AT muhammadsinan onsemianalyticalstudyoffractionalorderkawaharapartialdifferentialequationwiththehomotopyperturbationmethod AT kamalshah onsemianalyticalstudyoffractionalorderkawaharapartialdifferentialequationwiththehomotopyperturbationmethod AT zareenakhan onsemianalyticalstudyoffractionalorderkawaharapartialdifferentialequationwiththehomotopyperturbationmethod AT qasemalmdallal onsemianalyticalstudyoffractionalorderkawaharapartialdifferentialequationwiththehomotopyperturbationmethod AT fathallarihan onsemianalyticalstudyoffractionalorderkawaharapartialdifferentialequationwiththehomotopyperturbationmethod
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On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method

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