On the Theory and Applications of q-Mittag-Leffler-Laguerre Polynomials

In this work, we develop the theory of 2-variable q-Mittag-Leffler-Laguerre polynomials by employing a generating function that incorporates 0th- order q-Bessel Tricomi functions. We proceed to derive their se- ries definition and various properties. By applying the extended monomiality principle for q-polynomials, we establish the quasi-monomiality characteristics of these polynomials and explore additional features. Additionally, we determine the operational representations of the 2-variable q-Mittag-Leffler-Laguerre polynomials. We also introduce the mth order 2-variable q-Mittag-Leffler-Laguerre polynomials. Finally, this research concludes with the derivation of the 1-variable q-Mittag-Leffler-Laguerre polynomials, an analysis of their zero distributions, and a graphical representation of their properties.