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.
Kottakkaran Sooppy Nisar, Gauhar Rahman, Zivorad Tomovski
11991, Prince Sattam bin Abdulaziz University; International Islamic University; Institute of Mathematics
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
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