Optimal control of fractional diffusion equation

In this paper we apply the classical control theory to a fractional diffusion equation in a bounded domain. The fractional time derivative is considered in a Riemann-Liouville sense. We first study the existence and the uniqueness of the solution of the fractional diffusion equation in a Hilbert space. Then we show that the considered optimal control problem has a unique solution. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of right fractional Caputo derivative, we obtain an optimality system for the optimal control. (C) 2010 Elsevier Ltd. All rights reserved.