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

Abstract

In this article, we derive four theorems concerning the fractional integral image for the product of the $q$ -analogue of general class of polynomials with the $q$ -analogue of the $I$ -functions. To illustrate our main results, we use $q$ -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 $q$ -fractional integrals, as well as the relationship between the generalized Weyl type and the Weyl type $q$ -fractional integrals.