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On a more general fractional integration by parts formulae and applications

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dc.contributor.author Abdeljawad, Thabet
dc.contributor.author Atangana, Abdon
dc.contributor.author Gómez-Aguilar, J.F.
dc.contributor.author Jarad, Fahd
dc.date.accessioned 2022-10-04T13:02:14Z
dc.date.available 2022-10-04T13:02:14Z
dc.date.issued 2019-12-15
dc.identifier.citation Abdeljawad, Thabet...et al. (2019). "On a more general fractional integration by parts formulae and applications", Physica A: Statistical Mechanics and its Applications, Vol. 536. tr_TR
dc.identifier.issn 0378-4371
dc.identifier.uri http://hdl.handle.net/20.500.12416/5798
dc.description.abstract The integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators; thus, we develop fractional integration by parts for fractional integrals, Riemann–Liouville, Liouville–Caputo, Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. We allow the left and right fractional integrals of order α>0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case α=1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1016/j.physa.2019.122494 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Binomial Coefficients tr_TR
dc.subject Convolution tr_TR
dc.subject Fractional Calculus tr_TR
dc.subject Fractional Derivatives tr_TR
dc.subject New Integration by Parts tr_TR
dc.title On a more general fractional integration by parts formulae and applications tr_TR
dc.type article tr_TR
dc.relation.journal Physica A: Statistical Mechanics and its Applications tr_TR
dc.contributor.authorID 234808 tr_TR
dc.identifier.volume 536 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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