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

TL;DR

This paper investigates the total controllability of nonlocal semilinear functional evolution equations with non-instantaneous impulses and delays in Hilbert spaces, providing sufficient conditions and demonstrating their applicability through an example.

Contribution

It introduces new criteria for total controllability of complex evolution systems with impulses and delays, extending existing controllability concepts.

Findings

Established sufficient conditions for total controllability.

Proved total controllability for a class of functional integro-differential equations.

Provided an example demonstrating the practical feasibility of the results.

Abstract

In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equations 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 is given to demonstrate the feasibility of derived abstract results.