Preprint Article Version 1 This version is not peer-reviewed

Further Extension of Extended Fractional Derivative Operator of Riemann-Liouville

Version 1 : Received: 1 December 2017 / Approved: 4 December 2017 / Online: 4 December 2017 (04:21:01 CET)

How to cite: Rahman, G.; Mubeen, S.; Nisar, K.S. Further Extension of Extended Fractional Derivative Operator of Riemann-Liouville. Preprints 2017, 2017120013 (doi: 10.20944/preprints201712.0013.v1). Rahman, G.; Mubeen, S.; Nisar, K.S. Further Extension of Extended Fractional Derivative Operator of Riemann-Liouville. Preprints 2017, 2017120013 (doi: 10.20944/preprints201712.0013.v1).

Abstract

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

Subject Areas

hypergeometric function; extended hypergeometric function; mellin transform; fractional derivative; appell's function