A note on Wright-type generalized $q$-hypergeometric function

In 2001, Virchenko et al. published a paper on a new generalization of Gauss hypergeometric function, namely Wright-type generalized hypergeometric function. Present work aims to define the $q$-analogue generalized hypergeometric function, which reduces to generalized hypegeometric function by letting q tends to one, and study some new properties. Convergence of the series defining generalized $q$-hypergeometric function and properties including certain differentiation formulae and integral representations have been deduced.