On q-Gamma Operators and Their Applications to Classes of Bessel Functions

In this paper, we introduce two innovative variations of a gamma integral operator in the context of q-calculus theory. These q-analogues are derived from well-known q-analogues of the exponential function, with a focus on functions that satisfy specific exponential growth conditions. We also explore the application of these q-analogues in different categories of q-Bessel functions, including types one, two, and three. Furthermore, we derive various formulas and corollaries that demonstrate the practical applications of our findings. Additionally, we consider the finite products of Bessel functions of the same type in our analysis.