Regional controllability analysis of fractional diffusion equations with Riemann-Liouville time fractional derivatives

TL;DR

This paper investigates regional controllability of fractional diffusion systems with Riemann-Liouville derivatives, characterizing actuators and proposing an energy-efficient control approach with practical applications.

Contribution

It introduces a new analysis framework for regional controllability in fractional diffusion equations and develops a minimum energy control method with application examples.

Findings

Characterization of strategic actuators for regional controllability

Development of a minimum energy control approach

Successful application to two case studies

Abstract

This paper is concerned with the concepts of regional controllability for the Riemann-Liouville time fractional diffusion systems of order $\alpha\in(0,1)$. The characterizations of strategic actuators to achieve regional controllability are investigated when the control inputs emerge in the differential equations as distributed inputs. In the end, an approach to guarantee the regional controllability of the problems under consideration in the considered subregion with minimum energy control is described and successfully tested through two applications.