Bohr-Type Inequalities for Fractional Differential and Integral Operators

Abstract: We study Bohr type inequalities within the framework of fractional calculus. Using Riemann Liouville fractional differential and integral operators, we establish generalized Bohr radii for analytic functions in the unit disk, including the classes of univalent, convex, and Bloch functions. The results unify earlier cases, recover the classical Bohr inequality as a limiting instance, and show how the Bohr radius decreases with the fractional order. Numerical computations further illustrate how the radii vary with the fractional order, highlighting the transition from the classical to the fractional setting.