Geodesic
Cauchy fractional derivative
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 12 (2020) no. 4, pp. 28-32

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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, Cauchy's integral formula for derivatives.
Mots-clés : fractional calculus, Laplace transform 
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U. Kaya. Cauchy fractional derivative. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 12 (2020) no. 4, pp. 28-32. http://geodesic.mathdoc.fr/item/VYURM_2020_12_4_a2/