A Pontryagin maximum principle for optimal control problems involving generalized distributional-order derivatives

In this work, we extended fractional optimal control (OC) theory by proving a version of Pontryagin's maximum principle and establishing sufficient optimality conditions for an OC problem. The dynamical system constraint in the OC problem under investigation is described by a generalized fractional derivative: the left-sided Caputo distributed-order fractional derivative with an arbitrary kernel. This approach provides a more versatile representation of dynamic processes, accommodating a broader range of memory effects and hereditary properties inherent in diverse physical, biological, and engineering systems.