Cauchy fractional derivative

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.