Stability and controllability analysis of non–linear Volterra Fredholm Hammerstein impulsive integro–dynamic systems with delay on time scale

Abstract

The focus of this article is the examination of Volterra Fredholm Hammerstein type impulsive integro-dynamic systems, along with their corresponding fractional order systems, within the framework of a time scale domain that incorporates delays. The Banach Contraction Principle is employed to establish the existence and uniqueness of solutions for both types of problems. In order to address controllability in our proposed scenarios, we employ control functions and the Picard operator. We also verified the Hyers–Ulam stability using Grönwall's inequality on time scale. To demonstrate our findings, we include several illustrative examples.