Research Article On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method Muhammad Sinan , 1,2 Kamal Shah , 3 Zareen A. Khan , 4 Qasem Al-Mdallal , 5 and Fathalla Rihan 5 1 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China 2 Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtunkhwa, Pakistan 3 Department of Mathematics, University of Malakand, Chakdara Dir (L) 18000, Khyber Pakhtunkhwa, Pakistan 4 College of Science, Mathematical Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia 5 Department of Mathematical Sciences, UAE University, P.O. Box 15551, Al-Ain, UAE CorrespondenceshouldbeaddressedtoFathallaRihan;frihan@uaeu.ac.ae Received 7 August 2021; Revised 5 October 2021; Accepted 11 October 2021; Published 3 November 2021 AcademicEditor:NdolaneSene Copyright©2021MuhammadSinanetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Inthisstudy,weinvestigatethesemianalyticsolutionofthefifth-orderKawaharapartialdifferentialequation(KPDE)withthe approachoffractional-orderderivative.WeuseCaputo-typederivativetoinvestigatethesaidproblembyusingthehomotopy perturbationmethod(HPM)fortherequiredsolution.Weobtainthesolutionintheformofinfiniteseries.Wenexttriggered different parametric effects (such as x,t,andsoon)onthestructureofthesolitarywavepropagation,demonstratingthatthe breadthandamplitudeofthesolitarywavepotentialmayalterwhentheseparametersarechanged.Wehavedemonstratedthat He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation throughourcalculationsandsimulations.Wemayapplyourmethodtoanadditionalcomplicatedproblem,particularlyonthe 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. 1. Introduction PDEs have important applications in physics, engineering, and other applied sciences. ey can describe different phenomena and processes of real-world problems. One of theimportantKPDEarisesinthetheoryofmagnetoacoustic and shallow-water waves. Furthermore, it arises in the theory of shallow-water waves with surface tension and magnetoacoustic waves in plasmas. erefore, several ana- lytical and numerical methods have been established in literature to investigate the prosed problems of PDEs. For instance,[1]authorshaveusedthecomparisonmethodfor thesolutionofthefamousKawaharaequation.Inthesame line,aprocedurewasdevelopedin[2]fortheexactsolution of the said problem. Also, authors [3] have computed the solution of the Kawahara equation by using symbolic computation.Inthisstudy,weapplyasemianalyticHPMto solve the fifth-order KPDEs. As in the last several decades’ investigation, traveling-waves solutions for nonlinear equations played an important role in the study of the nonlinearphysicalphenomenon[4].ementionedmethod providesanefficientapproachtosolveanonlinearproblem. eKPDEwasfirstsuggestedbyKawahara[5]in1972.Since thesenonlinearequationsneedtobesolvedbyusingsome approximate methods, researchers have solved several nonlinear problems by using HPM. is method was first proposed by He [6] and has been applied in [7] for the solution of differential equations and integral equations in both linear and nonlinear cases. e said method is a combination of topological homotopy and traditional per- turbation methods. e advantage of this method is to provideananalyticapproximatesolutioninappliedsciences Hindawi Journal of Mathematics Volume 2021, Article ID 6045722, 11 pages https://doi.org/10.1155/2021/6045722