Saigo fractional q-integral operator for product of general class of q-polynomial and generalized q-Mittag-Leffler function

Saigo fractional q-integral operator

Abstract

This paper aims to derive the images of the generalized $q$-analogue of Mittag-Leffler functions, in which its argument contains a factor $x^{\rho} \left(xq^{-\lambda} +\xi \right)^{-\sigma} $, under the Saigo fractional $q$-integral operator. The derived findings are of a general nature and include special cases like Weyl $q$-integral operator, Kober $q$-integral operator, and Riemann-Liouville $q$-integral operator.