Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2019; 34(2): 507-522

Online first article February 8, 2019      Printed April 30, 2019

https://doi.org/10.4134/CKMS.c180140

Copyright © The Korean Mathematical Society.

On a certain extension of the Riemann-Liouville fractional derivative operator

Kottakkaran Sooppy Nisar, Gauhar Rahman, Zivorad Tomovski

11991, Prince Sattam bin Abdulaziz University; International Islamic University; Institute of Mathematics

Abstract

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al.~\cite{Choi2017}. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

Keywords: hypergeometric function, beta function, extended hypergeometric function, Mellin transform, fractional derivative, Appell's function

MSC numbers: 33C15, 33C05