Faber polynomial coefficients estimates for certain subclasses of $q$-Mittag-Leffler-Type analytic and bi-univalent functions

In this paper, we introduce the $q$-analogus of generalized differential operator involving $q$-Mittag-Leffler function in open unit disk

$$E=\left\{z:z\in \mathbb{C}\text{and}\left|z\right|<1\right\}$$

and define new subclass of analytic and bi-univalent functions. By applying the Faber polynomial expansion method, we then determined general coefficient bounds $|a_n|$, for $n\ge 3$. We also highlight some known consequences of our main results.