This paper investigates different forms of Hyers–Ulam stability for solutions of a nonlinear fractional hybrid dynamic equation defined on arbitrary time scales. By employing the measure of noncompactness together with a newly developed generalized version of Darbo’s fixed-point theorem, the existence of solutions is established. The uniqueness of solutions is further guaranteed via the Banach fixed-point theorem. In addition, illustrative numerical examples are presented to demonstrate the applicability and effectiveness of the theoretical results.