On generalized $\mathtt{k}$-fractional derivative operator

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