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We introduce a new optimal control problem where the controlled dynamicalsystem depends on multi-order (incommensurate) fractional differentialequations. The cost functional to be maximized is of Bolza type and depends onincommensurate Caputo fractional-orders derivatives. We establish continuityand differentiability of the state solutions with respect to perturbedtrajectories. Then, we state and prove a Pontryagin maximum principle forincommensurate Caputo fractional optimal control problems. Finally, we give anexample, illustrating the applicability of our Pontryagin maximum principle.

Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems