Fractional integral formulas involving generalized hypergeometric functions and general class of multivariable polynomial. (English) Zbl 1488.26024
Summary: The aim of this paper is to evaluate two theorems for the generalized fractional integration of arbitrary complex order involving the product of extended generalized hypergeometric function and a general class of multivariable polynomials. The considered generalized fractional integration operators contain the Appell function as a kernel and are introduced by Saigo and Maeda. The operators studied in this paper generalize the classical Riemann-Liouville, Weyl, Erdélyi-Kober and Saigo operators. Some interesting special cases of our main results are also considered.
MSC:
26A33 | Fractional derivatives and integrals |
33B15 | Gamma, beta and polygamma functions |
33C05 | Classical hypergeometric functions, \({}_2F_1\) |
33C15 | Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\) |
33C20 | Generalized hypergeometric series, \({}_pF_q\) |