Abstract
This paper deals with an external optimal control problem governed by coupled system of semilinear fractional parabolic equation and parabolic equation with Neumann exterior value condition. Under some assumptions on the nonlinearity, the well-posedness and boundedness of solutions for the system are proved. After showing the Lipschitz continuity and Fréchet differentiability of the control-to-state operator for the controlled system, we establish the existence theorem of solutions and the first-order necessary optimality conditions for an associated optimal control problem.
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