Numerical solution of a parabolic optimal control problem with time-fractional derivative

The article deals with a linear-quadratic optimal control problem governed by a parabolic equation with time-fractional derivative taken in Caputo definition. We impose pointwise constraints on state and control functions. The derivative in time of state function is taken in the Caputo derivative form of fractional order α ϵ (0,1). The mesh approximation is based on the using of finite-difference implicit scheme for the state equation. The Lagrange function's saddle point satisfies the saddle point problem. Uzawa-type iterative method for numerical solution is used. The results of numerical tests are presented.