Approximate controllability for fractional diffusion equations by   Dirichlet boundary control
  In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary conditions using the eigenfunction expansion. Next we also study the dual system and apply their results to prove (i) the regularity of the solution with non-smooth boundary conditions and (ii) approximate controllability. 
Kenichi Fujishiro
math.OC