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New Fractional Derivatives Applied to the Korteweg-De Vries and Korteweg-De Vries-Burger's Equations

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dc.contributor.author Saad, Khaled M.
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Atangana, Abdon
dc.date.accessioned 2020-03-26T08:21:06Z
dc.date.available 2020-03-26T08:21:06Z
dc.date.issued 2018-09
dc.identifier.citation Saad, Khaled M.; Baleanu, Dumitru; Atangana, Abdon, "New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burger's equations", Computational & Applied Mathematics. Vol. 37, No 4, pp. 5203,5216, (2018) tr_TR
dc.identifier.issn 0101-8205
dc.identifier.uri http://hdl.handle.net/20.500.12416/2743
dc.description.abstract In this paper, we extend the model of the Korteweg-de Vries (KDV) and Korteweg-de Vries-Burger's (KDVB) to new model time fractional Korteweg-de Vries (TFKDV) and time fractional Korteweg-de Vries-Burger's (TFKDVB) with Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville-Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB. tr_TR
dc.language.iso eng tr_TR
dc.publisher Springer Heidelberg tr_TR
dc.relation.isversionof 10.1007/s40314-018-0627-1 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Time Fractional Korteweg-De Vries tr_TR
dc.subject Time Fractional Korteweg-De Vries-Burger's tr_TR
dc.subject Q-Homotopy Analysis Transform Method tr_TR
dc.subject Liouville-Caputo tr_TR
dc.subject Caputo-Fabrizio tr_TR
dc.subject Atangana-Baleanu tr_TR
dc.title New Fractional Derivatives Applied to the Korteweg-De Vries and Korteweg-De Vries-Burger's Equations tr_TR
dc.type article tr_TR
dc.relation.journal Computational & Applied Mathematics tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 37 tr_TR
dc.identifier.issue 4 tr_TR
dc.identifier.startpage 5203 tr_TR
dc.identifier.endpage 5216 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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