Fractional Integral and Derivative Formulas by Using Marichev-Saigo-Maeda Operators Involving the S-Function

الملخص EN

We establish fractional integral and derivative formulas by using Marichev-Saigo-Maeda operators involving the S-function.

The results are expressed in terms of the generalized Gauss hypergeometric functions.

Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals and derivatives are presented.

Also we develop their composition formula by applying the Beta and Laplace transforms.

Further, we point out also their relevance.