In this paper, we introduce the q-analogue generalized Hermite polynomials of two variables. Some recurrence relations for these q-polynomials are derived.

The Bessel function is probably the best known special function, within pure and applied mathematics. In this paper, we introduce the generalized q-analogue Bessel matrix function of two variables. Some properties of this function, such as generating function, q-difference equation, and recurrence relations are obtained.

The q-Laguerre polynomials are important q-orthogonal polynomials whose applications and generalizations arise in many applications such as quantumgroup (oscillator algebra, etc.), q-harmonic oscillator and coding theory. In this paper, we introduce the q-analogue modified Laguerre polynomials and generalized modified Laguerre polynomials of one variable. Some recurrence relations and q-Laplace transforms for these polynomials are derived.

In this paper, the q-analogue modified Laguerre matrix polynomials of three variables are introduced as finite series and Some properties of these matrix polynomials are obtained.