Approximate controllability for fractional diffusion equations by interior control

Abstract

We consider the approximate controllability by interior control of a partial differential equation with time derivatives of non-integer order. First, we prove the well-posedness of the inhomogeneous problem for the controlled system. Next, we study the dual system and show a weak type of unique continuation property. Finally, we prove the approximate controllability.

Keywords:

• fractional diffusion equation
• initial value/boundary value problem
• approximate controllability

Acknowledgments

The first named author was granted by the Global COE programme and is supported by the FMSP programme at Graduate School of Mathematical Sciences of The University of Tokyo. The authors thank the anonymous referee for valuable and constructive comments.