Dynamic Event Triggered Impulsive Control of a Stochastic Time-Delay Fractional Order Rumor Propagation Model with Short Memory

The continuous spread of rumors can easily cause social panic, which has led to sustained attention to research on rumor control. This paper proposes a control method for the rumor diffusion process under noise interference, incorporating time delay and memory effect. A Caputo fractional order rumor propagation model with time delay and hybrid noise is firstly established. Then, given the limited availability of natural resources, we apply event-triggered impulsive control to manage the stochastic system. To preserve the non-locality of fractional calculus, we develop the corresponding stochastic fractional-order propagation model with short-term memory, then implement dynamic event-triggered impulsive control. Experiments demonstrate that, compared to static event-triggered impulse control, the dynamic approach not only achieves more effective system control but also reduces the number of triggering events, leading to resource conservation.