Submitted:
14 December 2017
Posted:
15 December 2017
You are already at the latest version
Abstract
The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.
Keywords:
beta function
; k-beta function
; hypergeometric function
; k-hypergeometric function
; Mellin transform
; fractional derivative
; Appell's function
; k-Mittag-Leffler function
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
