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

dc.contributor.authorSaad, Khaled M.
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorAtangana, Abdon
dc.contributor.authorID56389tr_TR
dc.date.accessioned2020-03-26T08:21:06Z
dc.date.available2020-03-26T08:21:06Z
dc.date.issued2018
dc.departmentÇankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractIn 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.en_US
dc.description.publishedMonth9
dc.identifier.citationSaad, 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)en_US
dc.identifier.doi10.1007/s40314-018-0627-1
dc.identifier.endpage5216en_US
dc.identifier.issn0101-8205
dc.identifier.issue4en_US
dc.identifier.startpage5203en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/2743
dc.identifier.volume37en_US
dc.language.isoenen_US
dc.publisherSpringer Heidelbergen_US
dc.relation.ispartofComputational & Applied Mathematicsen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectTime Fractional Korteweg-De Vriesen_US
dc.subjectTime Fractional Korteweg-De Vries-Burger'sen_US
dc.subjectQ-Homotopy Analysis Transform Methoden_US
dc.subjectLiouville-Caputoen_US
dc.subjectCaputo-Fabrizioen_US
dc.subjectAtangana-Baleanuen_US
dc.titleNew Fractional Derivatives Applied to the Korteweg-De Vries and Korteweg-De Vries-Burger's Equationstr_TR
dc.titleNew Fractional Derivatives Applied To the Korteweg-De Vries and Korteweg-De Vries-burger's Equationsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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