q-difference equations for the composite 2D q-Appell polynomials and their applications

The main aim of this article is to introduce a new class of composite 2D q-Appell polynomials and to study their properties. The generating function, series definition and some explicit relations for these polynomials are derived. These polynomials are studied from determinantal view point and their q-recurrence relations and q-difference equations are established. The composite 2D q-Bernoulli, q-Euler and q-Genocchi and composite q-Bernoulli–Euler, q-Bernoulli–Genocchi and q-Euler–Genocchi polynomials are studied as particular members of this class. Certain interesting examples are considered in terms of these members to give the applications of main results.