Fractional - Integral Operators for the Product of a - Polynomial and - Analogue of the - Functions and Their Applications

In this article, we derive four theorems concerning the fractional integral image for the product of the - analogue of general class of polynomials with the - analogue of the - functions. To illustrate our main results, we use - fractional integrals of Erdélyi–Kober type and generalized Weyl type fractional operators. The study concludes with a variety of results that can be obtained by using the relationship between the Erdélyi–Kober type and the Riemann–Liouville - fractional integrals, as well as the relationship between the generalized Weyl type and the Weyl type - fractional integrals.