Enlarged Controllability of Riemann-Liouville Fractional Differential Equations

TL;DR

This paper studies the control of fractional diffusion systems of Riemann-Liouville type, establishing conditions for exact enlarged controllability using the Hilbert uniqueness method and characterizing minimum energy controls.

Contribution

It introduces a novel approach to exact enlarged controllability for fractional diffusion systems and provides a characterization of minimum energy controls.

Findings

Proves exact enlarged controllability for zone and pointwise actuators.

Develops a penalization method for control optimization.

Characterizes minimum energy control for the systems.

Abstract

We investigate exact enlarged controllability for time fractional diffusion systems of Riemann-Liouville type. The Hilbert uniqueness method is used to prove exact enlarged controllability for both cases of zone and pointwise actuators. A penalization method is given and the minimum energy control is characterized.