Certain Subclasses of Bi-Univalent Functions Involving Caputo Fractional Derivatives with Bounded Boundary Rotation

In this paper, we introduce and investigate new subclasses of analytic bi-univalent functions defined via Caputo fractional derivatives with boundary rotation constraints. Utilizing the generalized operator Cȷϱ, which encompasses and extends classical operators such as the Salagean differential operator and the Libera–Bernardi integral operator, we establish sharp coefficient estimates for the initial Taylor Maclaurin coefficients of functions within these subclasses. Furthermore, we derive Fekete–Szegö-type inequalities that provide bounds on the second and third coefficients and their linear combinations involving a real parameter. Our approach leverages subordination principles through analytic functions associated with the classes Tς(ξ) and RΩȷ,ϱ(ϑ,ς,ξ), allowing a unified treatment of fractional differential operators in geometric function theory. The results generalize several known cases and open avenues for further exploration in fractional calculus applied to analytic function theory.