TY  - JOUR
AU  - Cruz, Fátima
AU  - Almeida, Ricardo
AU  - Martins, Natália
PY  - 2025
TI  - A Pontryagin maximum principle for optimal control problems involving generalized distributional-order derivatives
JO  - AIMS Mathematics
SP  - 11939
EP  - 11956
VL  - 10
IS  - 5
AB  - 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.
UR  - https://doi.org/10.3934/math.2025539
DO  - 10.3934/math.2025539