On generalized k-fractional derivative operator

The principal aim of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. This paper establishes some results related to the newly defined fractional operator such as the Mellin transform and the relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and the Wright hypergeometric functions.