Various controllability results for Fredholm-Volterra type stochastic elastic damped integro-differential systems with applications

The controllability results and availability of mild solutions for a class of stochastic integrodifferential systems with structural elastic damping including Fredholm-Volterra type in Banach spaces are the main topics of this article. The operator semigroup theory and the Banach fixed-point theorem are used to prove the existence of mild solution. To test the approximate controllability conclusions, sufficient conditions of controllability problems are then developed. Furthermore, under certain suitable assumptions, the trajectory controllability of the studied system is ascertained using generalized Gronwall's inequality. The existence of optimum control is demonstrated using Balder's theorem. The obtained theoretical results are finally shown using an example. To validate the practical implementation of the topic under study using the numerical simulation, a stochastic mathematical model of bridges and towers with elastic damping is introduced.