Cauchy Fractional Derivative

Ufuk Kaya

doi:10.14529/mmph200403

Authors

Ufuk Kaya Bitlis Eren University, Bitlis

DOI:

https://doi.org/10.14529/mmph200403

Keywords:

Weyl's fractional derivative, fractional calculus, Laplace transform, Cauchy's integral formula for derivatives

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^(α)(s) = L{(–1)⁽^α⁾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.