Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions

TL;DR

This paper establishes conditions under which fractional delay control systems with nonlocal conditions can be approximately controlled, using advanced mathematical tools like fractional operators and fixed point theorems.

Contribution

It introduces a new nonlocal control condition and develops a framework for approximate controllability of fractional control inclusions in Hilbert spaces.

Findings

Derived sufficient conditions for approximate controllability

Applied fixed point theorem to fractional control systems

Provided an example with fractional partial differential inclusion

Abstract

We introduce a nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions. Approximate controllability of a fractional control nonlocal delay quasilinear functional differential inclusion in a Hilbert space is studied. The results are obtained by using the fractional power of operators, multi-valued analysis, and Sadovskii's fixed point theorem. Main result gives an appropriate set of sufficient conditions for the considered system to be approximately controllable. As an example, a fractional partial nonlocal control functional differential inclusion is considered.