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The <i>q</i>-derivative and Hohlov operators have seen much use in recent years. First, numerous well-known principles of the <i>q</i>-derivative operator are highlighted and explained in this research. We then build a novel subclass of analytic and bi-univalent functions using the Hohlov operator and certain <i>q</i>-Chebyshev polynomials. A number of coefficient bounds, as well as the Fekete–Szegö inequalities and the second Hankel determinant are provided for these newly specified function classes.