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Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions

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dc.contributor.author Fernandez, Arran
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Srivastava, H. M.
dc.date.accessioned 2020-02-28T12:18:54Z
dc.date.available 2020-02-28T12:18:54Z
dc.date.issued 2019-02
dc.identifier.citation Fernandez, Arran; Baleanu, Dumitru; Srivastava, H. M., "Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions", Communications in Nonlinear Science And Numerical Simulation, Vol. 67, pp. 517-527, (2019). tr_TR
dc.identifier.issn 1007-5704
dc.identifier.uri http://hdl.handle.net/20.500.12416/2576
dc.description.abstract We consider an integral transform introduced by Prabhakar, involving generalised multi-parameter Mittag-Leffler functions, which can be used to introduce and investigate several different models of fractional calculus. We derive a new series expression for this transform, in terms of classical Riemann-Liouville fractional integrals, and use it to obtain or verify series formulae in various specific cases corresponding to different fractional-calculus models. We demonstrate the power of our result by applying the series formula to derive analogues of the product and chain rules in more general fractional contexts. We also discuss how the Prabhakar model can be used to explore the idea of fractional iteration in connection with semigroup properties. (C) 2018 Elsevier B.V. All rights reserved. tr_TR
dc.language.iso eng tr_TR
dc.publisher Elsevier Science BV tr_TR
dc.relation.isversionof 10.1016/j.cnsns.2018.07.035 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Fractional Calculus tr_TR
dc.subject Mittag-Leffler Functions tr_TR
dc.subject Prabhakar Operators tr_TR
dc.subject Convergent Series tr_TR
dc.title Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions tr_TR
dc.type article tr_TR
dc.relation.journal Communications in Nonlinear Science And Numerical Simulation tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 67 tr_TR
dc.identifier.startpage 517 tr_TR
dc.identifier.endpage 527 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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