Finite-time contractive stability for fractional-order impulsive systems with time delays

This article presents a new perspective on finite-time stability (FTS) and finite-time contractive stability (FTCS) for fractional-order impulsive system (FOIS) with dual delays that depend on both state and time. By integrating impulsive control theory with the Lyapunov function (LF) method, we establish comprehensive stability criteria for stabilizing and destabilizing impulses. We further apply these results to two types of fractional-order neural networks (FONNs): fractional-order delayed neural networks (FODNNs) and fractional-order Cohen–Grossberg neural networks (FOCGNNs), both incorporating dual delays and impulse phenomena. Numerical simulations rigorously validate our theoretical findings, demonstrating the effectiveness and practical relevance of the proposed approach.