Numerical Solutions to the Time-Fractional Swift–Hohenberg Equation Using Reproducing Kernel Hilbert Space Method

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dc.contributor.authorAttia, Nourhane
dc.contributor.authorAkgül, Ali
dc.contributor.authorSeba, Djamila
dc.contributor.authorNour, Abdelkader
dc.date.accessioned2024-12-24T19:10:19Z
dc.date.available2024-12-24T19:10:19Z
dc.date.issued2021
dc.departmentSiirt Üniversitesi
dc.description.abstractIn this work, a numerical approach based on the reproducing kernel theory is presented for solving the fractional Swift–Hohenberg equation (FS-HE) under the Caputo time-fractional derivative. Such equation is an effective model to describe a variety of phenomena in physics. The analytic and approximate solutions of FS-HE in the absence and presence of dispersive terms have been described by applying the reproducing kernel Hilbert space method (RKHSM). The benefit of the proposed method is its ability to get the approximate solution of the FS-HE easily and quickly. The current approach utilizes reproducing kernel theory, some valuable Hilbert spaces, and a normal basis. The theoretical applicability of the RKHSM is demonstrated by providing the convergence analysis. By testing some examples, we demonstrated the potentiality, validity, and effectiveness of the RKHSM. The computational results are compared with other available ones. These results indicate the superiority and accuracy of the proposed method in solving complex problems arising in widespread fields of technology and science. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
dc.identifier.doi10.1007/s40819-021-01132-0
dc.identifier.issn2349-5103
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85114439510
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org10.1007/s40819-021-01132-0
dc.identifier.urihttps://hdl.handle.net/20.500.12604/4026
dc.identifier.volume7
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofInternational Journal of Applied and Computational Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectCaputo fractional derivative
dc.subjectFractional Swift–Hohenberg equation
dc.subjectGram–Schmidt process
dc.subjectReproducing kernel Hilbert space method
dc.titleNumerical Solutions to the Time-Fractional Swift–Hohenberg Equation Using Reproducing Kernel Hilbert Space Method
dc.typeArticle

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