Exact Null Controllability of Non-Autonomous Conformable Fractional Semi-Linear Systems with Nonlocal Conditions

TL;DR

This paper investigates the precise control of certain non-autonomous fractional systems with nonlocal conditions, establishing conditions for exact null controllability using conformable fractional calculus and evolution operator theory.

Contribution

It introduces new controllability results for non-autonomous conformable fractional semi-linear systems with nonlocal conditions, relaxing typical assumptions like compactness or Lipschitz continuity.

Findings

Established existence of mild solutions under broad conditions

Provided sufficient criteria for exact null controllability

Illustrated results with a practical example

Abstract

We study the exact null controllability of a class of non-autonomous conformable fractional semi-linear evolution systems with nonlocal initial conditions in Hilbert spaces. The analysis is carried out within the framework of conformable fractional calculus and linear evolution operator theory. Under suitable assumptions, we establish the existence of mild solutions and provide sufficient conditions for exact null controllability. Notably, the nonlocal term is allowed to be continuous without requiring compactness or Lipschitz-type conditions. An example is included to illustrate the applicability of the main results.