Throughout the paper, we introduce a new subclass ${\mathcal{H}}_{\alpha ,\mu ,\rho ,m,\beta }^{n,q,\lambda ,l}f(z)$ by using the Bazilevič functions with the idea of bounded boundary rotation and $q$-analogue Cătaş operator. Also we find the estimate of the coefficients for functions in this class. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward $(p,q)$-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter $p$ is obviously redundant.