Controllability of higher order stochastic fractional control delay systems involving damping behavior

Highlights：

• This article focuses on the problem of controllability of both cases linear and nonlinear higher order stochastic fractional control delay systems with damping behavior, which involving Caputo fractional derivative. The significant contributions are specified as below:

• It is more essential to consider the fractional damped stochastic systems with higher order. Many of the previous results on lower order fractional stochastic systems are often for delay in state. So, it is crucial to pay attention to the study of higher order fractional stochastic systems which have control delay and damping behavior.

• Controllability Grammian matrix with Caputo fractional derivative is employed to developed the suitable conditions to impose that the linear fractional damped stochastic control delay system of order μ−1<ρ1≤μλ−1<ρ2≤λ is controllable.

• Besides, we formulated the controllability conditions for corresponding nonlinear fractional stochas- tic control delay system with damping behaviour by employing Burkholder-Davis-Gundys inequality and Banach fixed point theorem.

摘要

This article focuses on the problem of controllability of both cases linear and nonlinear higher order stochastic fractional control delay systems with damping behavior, which involving Caputo fractional derivative. The significant contributions are specified as below:•It is more essential to consider the fractional damped stochastic systems with higher order. Many of the previous results on lower order fractional stochastic systems are often for delay in state. So, it is crucial to pay attention to the study of higher order fractional stochastic systems which have control delay and damping behavior.•Controllability Grammian matrix with Caputo fractional derivative is employed to developed the suitable conditions to impose that the linear fractional damped stochastic control delay system of order μ−1<ρ1≤μλ−1<ρ2≤λ is controllable.•Besides, we formulated the controllability conditions for corresponding nonlinear fractional stochas- tic control delay system with damping behaviour by employing Burkholder-Davis-Gundys inequality and Banach fixed point theorem.