Approximate and Exact Solutions of Some Nonlinear Differential Equa-tions Using the Novel Coupling Approach in the Sense of Conformable Fractional Derivative

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dc.contributor.authorLiaqat, Muhammad Imran
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:33:56Z
dc.date.available2024-12-24T19:33:56Z
dc.date.issued2024
dc.departmentSiirt Üniversitesi
dc.description.abstractSeveral scientific fields utilize fractional nonlinear partial differential equations to model various phenomena. However, most of these equations lack exact solutions. Consequently, techniques for obtaining approximate solutions, which sometimes yield exact solutions, are essential. In this research, we develop a new approach by combining the homotopy perturbation method (HPM) and the conformable natural transform to solve the gas-dynamic equation (GDE), the Fokker-Planck equation (FPE), and the Swift-Hohenberg equation (SHE) in the context of conformable derivatives. The proposed approach is called the conformable natural homotopy perturbation method (CNHPM). This approach has the advantage of not requiring assumptions about significant or minor physical factors. Consequently, it eliminates some of the constraints associated with conventional perturbation methods and can solve both weak and highly nonlinear problems. We consider the absolute, relative, and residual errors numerically and graphically to assess the correctness of our approach. The results show that our approach serves as a suitable alternative to the approximate methods in the literature for solving fractional differential equations.
dc.identifier.doi10.37256/cm.5420245244
dc.identifier.endpage4160
dc.identifier.issn2705-1064
dc.identifier.issn2705-1056
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85207242583
dc.identifier.scopusqualityQ4
dc.identifier.startpage4132
dc.identifier.urihttps://doi.org/10.37256/cm.5420245244
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8335
dc.identifier.volume5
dc.identifier.wosWOS:001352635600002
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherUniversal Wiser Publisher
dc.relation.ispartofContemporary Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectfokker-planck equation
dc.subjectgas-dynamic equation
dc.subjectswift-hohenberg equation
dc.subjectapproximate solutions
dc.subjectexact solutions
dc.titleApproximate and Exact Solutions of Some Nonlinear Differential Equa-tions Using the Novel Coupling Approach in the Sense of Conformable Fractional Derivative
dc.typeArticle

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