A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Function

Manish Kumar Bansal; Devendra Kumar∗; Rashmi Jain

doi:10.5666/KMJ.2019.59.3.433

Article

KYUNGPOOK Math. J. 2019; 59(3): 433-443

Published online September 23, 2019

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Function

Manish Kumar Bansal, Devendra Kumar∗, Rashmi Jain

Department of Applied Science, Govt. Engineering College, Banswara 327001, Rajasthan, India
e-mail : bansalmanish443@gmail.com
Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
e-mail : devendra.maths@gmail.com
Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, Rajasthan, India
e-mail : rashmiramessh1@gmail.com

Received: July 30, 2017; Revised: December 17, 2018; Accepted: December 20, 2018

Abstract

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Abstract

In this work, we evaluate the Mellin transform of the Marichev-Saigo-Maeda fractional integral operator with Appell’s function F₃ type kernel. We then discuss six special cases of the result involving the Saigo fractional integral operator, the Erdélyi-Kober fractional integral operator, the Riemann-Liouville fractional integral operator and the Weyl fractional integral operator. We obtain new and known results as special cases of our main results. Finally, we obtain the images of S-generalized Gauss hypergeometric function under the operators of our study.

Keywords: S-Generalized Gauss hypergeometric function, Marichev-SaigoMaeda fractional integral operators, Appell’s function, Mellin transform.