An alternative definition for the k-Riemann-Liouville fractional derivative

Abstract

Copyright c © 2014 Gustavo Abel Dorrego. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This work is dedicated to Dr. Rubén A. Cerutti The aim of this paper is to introduce an alternative definition for the k-Riemann-Liouville fractional derivative given in [6] and whose ad-vantage is that it is the left inverse of the corresponding of k-Riemann-Liouville fractional integral operator introduced by [5]. Its basic prop-erties are discussed, their Laplace transform, the derivative of the po-tential function and the derivative of the Mittag-Leffler k-function in-troduced in [2] is calculated.