dc.contributor.author |
Baleanu, Dumitru
|
|
dc.contributor.author |
Fernandez, Arran
|
|
dc.contributor.author |
Akgül, Ali
|
|
dc.date.accessioned |
2021-01-29T11:15:27Z |
|
dc.date.available |
2021-01-29T11:15:27Z |
|
dc.date.issued |
2020-03 |
|
dc.identifier.citation |
Baleanu, Dumitru; Fernandez, Arran; Akgul, Ali (2020). "On a Fractional Operator Combining Proportional and Classical Differintegrals", Mathematics, Vol. 8, no. 3. |
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dc.identifier.issn |
2227-7390 |
|
dc.identifier.uri |
http://hdl.handle.net/20.500.12416/4513 |
|
dc.description.abstract |
The 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 <mml:semantics>f(t)</mml:semantics>, by a fractional integral operator applied to the derivative <mml:semantics>f ' (t)</mml:semantics>. We define a new fractional operator by substituting for this <mml:semantics>f ' (t)</mml:semantics> 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. |
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dc.language.iso |
eng |
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dc.relation.isversionof |
10.3390/math8030360 |
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dc.rights |
info:eu-repo/semantics/openAccess |
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dc.subject |
Fractional Integrals |
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dc.subject |
Caputo Fractional Derivatives |
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dc.subject |
Fractional Differential Equations |
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dc.subject |
Bivariate Mittag-Leffler Functions |
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dc.subject |
26A33 |
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dc.subject |
34A08 |
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dc.title |
On a Fractional Operator Combining Proportional and Classical Differintegrals |
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dc.type |
article |
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dc.relation.journal |
Mathematics |
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dc.contributor.authorID |
56389 |
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dc.identifier.volume |
8 |
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dc.identifier.issue |
3 |
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dc.contributor.department |
Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü |
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