On the approximate controllability from the boundary for fractional wave equations
Mahamadi Warma · Applicable Analysis · 2016
We study the boundary controllability of fractional wave (also known as super diffusion) equations associated to the Caputo fractional derivative with a symmetric non-negative uniformly elliptic operator subject to the non-homogeneous Dirichlet- or Robin-type boundary conditions. Our results show that if and is a connected bounded open set with smooth boundary , then the system in , on , , , is approximately controllable for any , , any non-empty open set and any , where in the case of the Dirichlet boundary condition and for the Robin boundary conditions. Here denotes the dual of the domain of the fractional power of order of the realization in of the operator A with the zero boundary conditions on . The results obtained in the article are optimal given that such a system cannot be null controllable.