  We consider distributed-order non-local fractional optimal control problems
with controls taking values on a closed set and prove a strong necessary
optimality condition of Pontryagin type. The possibility that admissible
controls are subject to pointwise constraints is new and requires more
sophisticated techniques to include a maximality condition. We start by proving
results on continuity of solutions due to needle-like control perturbations.
Then, we derive a differentiability result on the state solutions with respect
to the perturbed trajectories. We end by stating and proving the Pontryagin
maximum principle for distributed-order fractional optimal control problems,
illustrating its applicability with an example.
