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

• Bansal, Manish Kumar (Department of Applied Science, Govt. Engineering College) ;
• Kumar, Devendra (Department of Mathematics, University of Rajasthan) ;
• Jain, Rashmi (Department of Mathematics, Malaviya National Institute of Technology)
• Accepted : 2018.12.20
• Published : 2019.09.23
• 13 2

#### Abstract

In this work, we evaluate the Mellin transform of the Marichev-Saigo-Maeda fractional integral operator with Appell's function $F_3$ type kernel. We then discuss six special cases of the result involving the Saigo fractional integral operator, the $Erd{\acute{e}}lyi$-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-Saigo-Maeda fractional integral operators;Appell's function;Mellin transform

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