Mittag-Leffler-Gegenbauer polynomials of two variable: Symbolic operator approach

n this paper, we employ the symbolic operator approach, a versatile tool for studying and generalizing special functions, to introduce a novel class of polynomials, the Two-Variable Mittag-Le er-Gegenbauer polynomials. This family generalizes several classical polynomials, including Laguerre, Hermite, and Gegenbauer olynomials, providing a unifying framework for their analysis.We investigate the main properties of our polynomials, including series representations, generating functions, operational rules, and relations via fractional integrals and derivatives. The practical relevance is illustrated through numerical examples and graphical demonstrations. Additionally, we explore an application to fractional kinetic equations, highlighting how these polynomials naturally model memory-dependent processes and reveal new features in fractional dynamics. Overall, this work demonstrates that the combination of symbolic operators and a two-variable structure provides a powerful framework for generating, analysing, and applying new classes of special polynomials in both theoretical and applied settings