On the Fractional q-Differintegral Operator for Subclasses of Bi-univalent Functions Subordinate to q-Ultraspherical Polynomials

In this paper, we introduce a novel class of bi-univalent functions using the fractional q-differintegral operator and q-ultraspherical polynomials. We examine the Taylor-Maclaurin coefficients |♭2| and |♭3| for functions in this new class. We also establish Fekete-Szeg¨o functional inequalities relevant to this subclass. By varying the parameters in our main results, we derive several new findings that contribute to the theoretical development of the field.