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 RiemannLiouville 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.
optimal control fractional differential equation transposition method