  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.
