Optimal controllability for multi-term time-fractional stochastic systems with non-instantaneous impulses (Q6633165)

In this paper, an optimal control problem for a system described by a fractional stochastic differential equation with non-instantaneous impulses is considered. The nonlocal properties of the system are captured by fractional-order derivatives in the Caputo sense, randomness is modeled using stochastic processes, and non-instantaneous impulses are represented by signals acting over finite intervals. A performance index is provided, and constraints on the controls are imposed.\N\NThe authors establish the existence of mild solutions using semigroup theory, stochastic techniques and Krasnoselskii's fixed-point theorem. Under natural assumptions, and with the use of a minimizing sequence, they prove the existence of an optimal state-control pair for the problem under consideration.\N\NTwo examples illustrate the application of the obtained results. The findings of this paper are applicable to various practical problems across multiple fields, including drug diffusion in the human body, population dynamics, theoretical physics, mathematical economics, chemical technology, industrial robotics, and engineering.