Controllability Properties for Equations with Memory of Fractional Type

Abstract

We study a general class of control systems with memory, which in particular includes systems with fractional derivatives and integrals and also the standard heat equation. We prove that the approximate controllability property of the heat equation is inherited by every system with memory in this class while controllability to zero is a singular property, which holds solely in the special case that the system indeed reduces to the standard heat equation. * This papers fits into the research program of the GNAMPA-INDAM.