Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika"
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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2020, Volume 12, Issue 4, Pages 28–32
DOI: https://doi.org/10.14529/mmph200403 (Mi vyurm461) 		 
Mathematics

Cauchy fractional derivative

U. Kaya

Bitlis Eren University, Bitlis, Turkey
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DOI: https://doi.org/10.14529/mmph200403
Abstract: In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula $F^{(\alpha)}(s) = L\{(-1)^{(\alpha)}L^{-1}\{F(s)\}\}$. Also, we find a relation between Weyl's fractional derivative and the formula above. Finally, we give some examples for fractional derivative of some elementary functions.
Keywords: Weyl's fractional derivative, fractional calculus, Laplace transform, Cauchy's integral formula for derivatives.
Received: 04.09.2020
Document Type: Article
MSC: 26A33, 30E20
Language: English
Citation: U. Kaya, “Cauchy fractional derivative”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 12:4 (2020), 28–32
Citation in format AMSBIB
\Bibitem{Kay20}
\by U.~Kaya
\paper Cauchy fractional derivative
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2020
\vol 12
\issue 4
\pages 28--32
\mathnet{http://mi.mathnet.ru/vyurm461}
\crossref{https://doi.org/10.14529/mmph200403}
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