A Study of Marichev-Saigo-Maeda Fractional Integral Opera- tors Associated with the S-Generalized Gauss Hypergeometric Function
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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 Erdelyi- 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.
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 Erdelyi- 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.
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