Controllability of a second-order non-autonomous stochastic semilinear system with several delays in control

This paper studies a second-order non-autonomous semilinear stochastic differential equation with several constant point delays in control. We prove the mild solution's existence and uniqueness using the semigroup theory of bounded linear operators, evolution family, stochastic analysis techniques, and Banach contraction principle. Our goal is to discuss various types of controllability of the stochastic semi linear system with the associated linear system. In the end, an example is included as an application to demonstrate the result. (c) 2021 Elsevier Ltd. All rights reserved.