On a Fractional Operator Combining Proportional and Classical Differintegrals

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dc.authoridFernandez, Arran/0000-0002-1491-1820
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorFernandez, Arran
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:33:42Z
dc.date.available2024-12-24T19:33:42Z
dc.date.issued2020
dc.departmentSiirt Üniversitesi
dc.description.abstractThe Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function f(t), by a fractional integral operator applied to the derivative f ' (t). We define a new fractional operator by substituting for this f ' (t) a more general proportional derivative. This new operator can also be written as a Riemann-Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann-Liouville integral and a Caputo derivative. We then conduct some analysis of the new definition: constructing its inverse operator and Laplace transform, solving some fractional differential equations using it, and linking it with a recently described bivariate Mittag-Leffler function.
dc.identifier.doi10.3390/math8030360
dc.identifier.issn2227-7390
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85082432609
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math8030360
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8242
dc.identifier.volume8
dc.identifier.wosWOS:000524085900059
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofMathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectfractional integrals
dc.subjectCaputo fractional derivatives
dc.subjectfractional differential equations
dc.subjectbivariate Mittag-Leffler functions
dc.subject26A33
dc.subject34A08
dc.titleOn a Fractional Operator Combining Proportional and Classical Differintegrals
dc.typeArticle

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