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Classes of operators in fractional calculus: A case study

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dc.contributor.author Fernandez, Arran
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2022-03-24T12:05:19Z
dc.date.available 2022-03-24T12:05:19Z
dc.date.issued 2021-07-30
dc.identifier.citation Fernandez, Arran; Baleanu, Dumitru (2021). "Classes of operators in fractional calculus: A case study", Mathematical Methods in the Applied Sciences, Vol. 44, No. 11, pp. 9143-9162. tr_TR
dc.identifier.issn 1099-1476
dc.identifier.uri http://hdl.handle.net/20.500.12416/5191
dc.description.abstract The notion of general classes of operators has recently been proposed as an approach to fractional calculus that respects pure and applied viewpoints equally. Here we demonstrate this approach as it applies to the operators with three-parameter Mittag-Leffler kernels defined by Prabhakar in 1971. By considering the general such operator as a class, we are able to better understand its fundamental nature and the different special cases that emerge. In particular, we show that many other named models of fractional calculus can fit within the class of operators defined by Prabhakar and that this class contains both singular and nonsingular operators together. We characterise completely the cases in which these operators are singular or nonsingular and the cases in which they can be written as finite or infinite sums of Riemann-Liouville differintegrals, to obtain finally a catalogue of subclasses with different types of properties. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1002/mma.7341 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.title Classes of operators in fractional calculus: A case study tr_TR
dc.type article tr_TR
dc.relation.journal Mathematical Methods in the Applied Sciences tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 44 tr_TR
dc.identifier.issue 11 tr_TR
dc.identifier.startpage 9143 tr_TR
dc.identifier.endpage 9162 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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