Solvability and optimal controls of non-instantaneous impulsive stochastic fractional differential equation of order q ∈ (1,2)

In this article, we study the stochastic fractional optimal control problem for a system governed by a class of non-instantaneous impulsive stochastic fractional differential equation in the infinite-dimensional spaces. We utilize the fractional calculus, stochastic analysis theory and a suitable fixed point approach to present the solvability of the stochastic fractional system. Then, the existence of optimal state-control pairs of the Lagrange problem is derived without uniqueness of solutions of the stochastic system. Finally, the main results are validated with the aid of an example.

Automated summary

This article studies the stochastic fractional optimal control problem in infinite-dimensional spaces governed by a class of non-instantaneous impulsive stochastic fractional differential equation. The solvability of the stochastic fractional system is presented using fractional calculus, stochastic analysis theory, and a suitable fixed point approach. The existence of optimal state-control pairs of the Lagrange problem is derived without requiring uniqueness of solutions of the stochastic system, and the main results are validated with an example.