Total controllability of nonlocal semilinear functional evolution equations with non-instantaneous impulses

Abstract

In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equation with non-instantaneous impulses and finite delay in Hilbert spaces. A set of sufficient conditions of total controllability is obtained for the evolution system under consideration by imposing the theory of \(C_0\)-semigroup and Banach fixed point theorem. We also established the total controllability results for a functional integro-differential equation. Finally, an example demonstrates the feasibility of derived abstract results.