Structural Properties and Applications of Generalized Fractional Multivariate q-Laguerre Polynomials

We introduce and develop a new class of Generalized Multivariate Fractional q-Laguerre Polynomials (GMFQLP), extending classical q-Laguerre families into a fractional and multivariate setting. Rigorous proofs are provided for generating functions, operational identities, and fractional q-difference equations. Explicit fractional q-integral operators are defined and analyzed. Applications to orthogonality, asymptotics, and Volterra-type integral equations are established. Numerical and graphical results are presented for zeros and structural patterns. This work unifies several existing theories and provides new avenues for quantum calculus and approximation theory.