Intermittent stabilization for the spatial-multiple-fractional advection–diffusion–reaction system with time-varying delay driven by Brown motion

Abstract

We consider the mean square exponential stabilization for the stochastic delay spatial-multiple-fractional advection–diffusion–reaction system (SDSMFADRS). A distributed controller discretely located in the space domain is firstly proposed, which can lessen the dependence of the state information of SDSMFADRS. Based on this distributed controller, an aperiodically intermittent controller is designed to reduce the time expenses. Using the Lyapunov functional method, the sufficient conditions of stability are established with the help of the improved fractional Poincare’s inequality. Besides, the impact of the space domain’s division, the control gain, the distributed controller’s location, the intermittent controller’s control ratio and the fractional order on the stability are investigated. The above results can be applied to the control problem of the groundwater pollution, and numerical examples are given to show the effectiveness of the designed controllers.