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Mathematics
Cauchy fractional derivative
U. Kaya Bitlis Eren University, Bitlis, Turkey
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
Citation:
U. Kaya, “Cauchy fractional derivative”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 12:4 (2020), 28–32
Linking options:
https://www.mathnet.ru/eng/vyurm461 https://www.mathnet.ru/eng/vyurm/v12/i4/p28
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Statistics & downloads: |
Abstract page: | 99 | Full-text PDF : | 35 | References: | 25 |
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