Controllability of partially observed stochastic semilinear fractional control systems

The study examines sufficient conditions for the stochastic controllability of a partially observed semilinear fractional-order stochastic control system. Employing the separation principle, we partition the system into two distinct forms: a linear stochastic control system and a semilinear deterministic control system. Our main results are derived through the application of Gronwall’s inequality, the Lipschitz condition, and the Cauchy sequence. Notably, this approach relaxes the requirements for the compactness of a strongly continuous semigroup and the boundedness of nonlinearity. To illustrate this concept, an example is provided.