Optimal control of a nonhomogeneous Dirichlet boundary fractional diffusion equation

We study a nonhomogeneous Dirichlet boundary fractional diffusion equation in a bounded domain. The fractional time derivative is considered in the Riemann-Liouville sense. We first prove by transposition the existence and the uniqueness of the solution of the boundary fractional diffusion equation. Then under some appropriate assumptions on the closed convex set of the admissible controls, we obtain a decoupled optimality system.