Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel

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dc.contributor.authorYavuz, Mehmet
dc.contributor.authorOzdemir, Necati
dc.contributor.authorBaskonus, Haci Mehmet
dc.date.accessioned2024-02-23T14:26:24Z
dc.date.available2024-02-23T14:26:24Z
dc.date.issued2018
dc.departmentNEÜen_US
dc.description.abstractIn this paper, time-fractional partial differential equations (FPDEs) involving singular and nonsingular kernel are considered. We have obtained the approximate analytical solution for linear and nonlinear FPDEs using the Laplace perturbation method (LPM) defined with the Liouville-Caputo (LC) and Atangana-Baleanu (AB) fractional operators. The AB fractional derivative is defined with the Mittag-Leffler function and has all the properties of a classical fractional derivative. In addition, the AB operator is crucial when utilizing the Laplace transform (LT) to get solutions of some illustrative problems with initial condition. We show that the mentioned method is a rather effective and powerful technique for solving FPDEs. Besides, we show the solution graphs for different values of fractional order a, distance term x and time value t. The classical integer-order features are fully recovered if a is equal to 1.en_US
dc.description.sponsorshipBalikesir University Scientific Research Projects Unit [BAP:2018/065]en_US
dc.description.sponsorshipThis research was supported by Balikesir University Scientific Research Projects Unit, BAP:2018/065.en_US
dc.identifier.doi10.1140/epjp/i2018-12051-9
dc.identifier.issn2190-5444
dc.identifier.issue6en_US
dc.identifier.scopus2-s2.0-85048160634en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1140/epjp/i2018-12051-9
dc.identifier.urihttps://hdl.handle.net/20.500.12452/14163
dc.identifier.volume133en_US
dc.identifier.wosWOS:000434469300002en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer Heidelbergen_US
dc.relation.ispartofEuropean Physical Journal Plusen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subject[Keyword Not Available]en_US
dc.titleSolutions of partial differential equations using the fractional operator involving Mittag-Leffler kernelen_US
dc.typeArticleen_US

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