Approximate controllability of a parabolic dynamic equation on homogeneous time scales

This paper aims to explore the approximate controllability of a semilinear system of parabolic dynamic equations on homogeneous time scales. Building on the innovative semigroup theory for time scales introduced in [13], we leverage a pivotal lemma from [5] that characterizes these semigroups. By combining these tools with Rothe’s fixed-point theorem, we provide a comprehensive framework to establish our results, bridging concepts from time scale calculus and control theory.