On The Class Of \(2D\) \(q\)-Appell Polynomials

In this research, as the new results of our previously proposed definition for the new class of \(2D\) \(q\)-Appell polynomials, we derive some interesting relations including the recurrence relation and partial \(q\)-difference equation of the aforementioned family of \(q\)-polynomials. Next, as some famous examples of this new defined class of \(q\)-polynomials, we obtain the corresponding relations to the \(2D\) \(q\)-Bernoulli polynomials, \(2D\) \(q\)-Euler polynomials as well as \(2D\) \(q\)-Genocchi polynomials.