Geometric Properties of the Normalized Fractional Bessel-Maitland Function Associated with the Riemann–Liouville Fractional Derivative

In this paper, we introduce and investigate a normalized fractional Bessel–Maitland function generated through the Riemann–Liouville fractional derivative, thereby establishing a new connection between fractional calculus and geometric function theory. By combining coefficient estimates with suitable inequalities involving the Gamma and digamma functions and appropriate monotonicity properties, we derive sufficient conditions ensuring that the proposed function belongs to several important subclasses of analytic and univalent functions, including uniformly convex, starlike, convex, k-uniformly starlike, k-uniformly convex, exponential, and lemniscate classes. We further examine structural properties of the associated coefficient sequence and provide numerical illustrations depicting the theoretical results. The proposed fractional normalization extends the classical generalized Bessel–Maitland and Wright-type functions and offers a unified framework for investigating their geometric behaviour under fractional differential operators, opening new directions for the study of special functions in geometric function theory and fractional calculus.