  Optimal Dirichlet boundary control for a fractional/normal evolution with a
final observation is considered. The unique existence of the solution and the
first-order optimality condition of the optimal control problem are derived.
The convergence of a temporally semidiscrete approximation is rigorously
established, where the control is not explicitly discretized and the state
equation is discretized by a discontinuous Galerkin method in time. Numerical
results are provided to verify the theoretical results.
