(untitled) (European Journal of Pure and Applied Mathematics, 2026)
Motivated by the interplay between -calculus and geometric function theory, this paper introduces and investigates a new subclass of bi-univalent functions associated with shell-like curves defined via the -Rabotnov function and the -analogue of Fibonacci numbers. By employing the subordination principle, we derive coefficient bounds for the initial Taylor–Maclaurin coefficients, specifically |a_2| and |a_3|, and further establish sharp Fekete–Szegö type inequalities for the proposed function class. Our results not only extend and generalize several recent contributions in the theory of bi-univalent functions but also highlight novel connections between -special functions, shell-like domains, and analytic inequalities. The findings presented herein contribute to a deeper understanding of the structural properties of bi-univalent functions and open avenues for future applications in operator theory and related analytic frameworks.