Hyers-Ulam Stability Analysis of an Impulsive Fractional Dynamic Equation with Nonlocal Initial Condition on Timescales

This chapter is centered on exploring the diverse aspects of Hyers-Ulam stability analysis for an impulsive fractional dynamic equation defined on timescales. The equation incorporates a nonlocal initial condition and is investigated utilizing the Caputo nabla ( \(\nabla \) ) derivative. The existence of a solution is established by employing the nonlinear versions of Leray-Schauder’s fixed-point theorem. Furthermore, the Banach fixed-point theorem is utilized to guarantee the uniqueness of the solution. To exemplify the practical application of the theoretical results, an illustrative example is presented.