Approximate Controllability of Fractional Nonlocal Delay Semilinear Systems in Hilbert Spaces

TL;DR

This paper investigates the approximate controllability of fractional nonlocal delay semilinear systems in Hilbert spaces, employing advanced mathematical tools to establish conditions for control and providing illustrative examples.

Contribution

It introduces new sufficient conditions for approximate controllability of fractional nonlocal delay systems using semigroup theory and fixed point methods.

Findings

Established sufficient conditions for approximate controllability.

Utilized semigroup theory and Schauder's fixed point theorem.

Provided an example illustrating the theoretical results.

Abstract

We study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a Hilbert space. The results are obtained by using semigroup theory, fractional calculus, and Schauder's fixed point theorem. Multi-delay controls and a fractional nonlocal condition are introduced. Furthermore, we present an appropriate set of sufficient conditions for the considered fractional nonlocal multi-delay control system to be approximately controllable. An example to illustrate the abstract results is given.