A Utilization of Liouville–Caputo Fractional Derivatives for Families of Bi-Univalent Functions Associated with Specific Holomorphic Symmetric Function

In this investigation, two new subfamilies of bi-univalent functions defined on the open unit disk are presented using Liouville–Caputo fractional derivatives. We determine bounds on the initial Maclaurin coefficients |a2| and |a3|, as well as Fekete–Szegö inequality results based on the bonds of a2 and a3 for functions belonging to certain bi-univalent function subfamilies. Additionally, some novel subfamilies are inferred that have not yet been examined within the context of Liouville–Caputo fractional derivatives.