Preprint Article Version 1 This version not peer reviewed

On Generalized k-Fractional Derivative Operator

Version 1 : Received: 14 December 2017 / Approved: 15 December 2017 / Online: 15 December 2017 (06:44:08 CET)

How to cite: Rahman, G.; Nisar, K.S.; Mubeen, S. On Generalized k-Fractional Derivative Operator. Preprints 2017, 2017120101 (doi: 10.20944/preprints201712.0101.v1). Rahman, G.; Nisar, K.S.; Mubeen, S. On Generalized k-Fractional Derivative Operator. Preprints 2017, 2017120101 (doi: 10.20944/preprints201712.0101.v1).

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.

Subject Areas

beta function; k-beta function; hypergeometric function; k-hypergeometric function; Mellin transform; fractional derivative; Appell's function; k-Mittag-Leffler function

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