Fundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and application to nonlinear dispersive wave model

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dc.contributor.authorYavuz, Mehmet
dc.contributor.authorSene, Ndolane
dc.date.accessioned2024-02-23T14:12:55Z
dc.date.available2024-02-23T14:12:55Z
dc.date.issued2021
dc.departmentNEÜen_US
dc.description.abstractBefore going further with fractional derivative which is constructed by Rabotnov exponential kernel, there exist many questions that are not addressed. In this paper, we try to recapitulate all the fundamental calculus, which we can obtain with this new fractional operator. The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions, polynomial functions, exponential functions, trigonometric functions, or Mittag-Leffler functions. For all the fractional differential equations, the obtained solutions are represented graphically. The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations. Finally, we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel. (c) 2020 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )en_US
dc.description.sponsorshipTUBITAK (The Scientific and Technological Research Council of Turkey)en_US
dc.description.sponsorshipM. Yavuz was supported by TUBITAK (The Scientific and Technological Research Council of Turkey).en_US
dc.identifier.doi10.1016/j.joes.2020.10.004
dc.identifier.endpage205en_US
dc.identifier.issn2468-0133
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85103663537en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage196en_US
dc.identifier.urihttps://doi.org/10.1016/j.joes.2020.10.004
dc.identifier.urihttps://hdl.handle.net/20.500.12452/12244
dc.identifier.volume6en_US
dc.identifier.wosWOS:000639471300007en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofJournal Of Ocean Engineering And Scienceen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectFractional Differential Equationen_US
dc.subjectNonlinear Dispersive Wave Modelen_US
dc.subjectRabotnov Exponential Kernelen_US
dc.subjectMittag-Leffler Functionen_US
dc.subjectLaplace Transformationen_US
dc.titleFundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and application to nonlinear dispersive wave modelen_US
dc.typeArticleen_US

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