A hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations

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dc.authoridUllah, Aman/0000-0003-4021-3599
dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.contributor.authorAhmad, Shabir
dc.contributor.authorUllah, Aman
dc.contributor.authorAkgul, Ali
dc.contributor.authorJarad, Fahd
dc.date.accessioned2024-12-24T19:34:00Z
dc.date.available2024-12-24T19:34:00Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractIt is important to deal with the exact solution of nonlinear PDEs of non-integer orders. Integral transforms play a vital role in solving differential equations of integer and fractional orders. 'o obtain analytical solutions to integer and fractional-order DEs, a few transforms, such as Laplace transforms, Sumudu transforms, and Elzaki transforms, have been widely used by researchers. We propose the Yang transform homotopy perturbation (YTHP) technique in this paper. We present the relation of Yang transform (YT) with the Laplace transform. We find a formula for the YT of fractional derivative in Caputo sense. We deduce a procedure for computing the solution of fractional-order nonlinear PDEs involving the power-law kernel. We show the convergence and error estimate of the suggested method. We give some examples to illustrate the novel method. We provide a comparison between the approximate solution and exact solution through tables and graphs.
dc.identifier.doi10.3934/math.2022521
dc.identifier.endpage9404
dc.identifier.issn2473-6988
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85127068844
dc.identifier.scopusqualityQ1
dc.identifier.startpage9389
dc.identifier.urihttps://doi.org/10.3934/math.2022521
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8383
dc.identifier.volume7
dc.identifier.wosWOS:000770060600004
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofAims Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectYang transform
dc.subjecthomotopy perturbation method
dc.subjectpower law kernel
dc.titleA hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations
dc.typeArticle

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