Fractional exponential stability of nonlinear conformable fractional-order delayed systems with delayed impulses and its application

This article studies the fractional exponential stability (FES) of nonlinear conformable fractional-order delayed systems (CFODSs) and the fractional exponential synchronization of conformable fractional-order delayed inertial neural networks (CFODINNs), both with delayed impulses (DIs). Under the conformable fractional-order derivative framework, a novel Halanay inequality is established by generalizing the average impulsive interval (AII), which is a key basis for further investigations. Additionally, based on the proposed inequality, the requirement of the magnitude relationship among the system delay, the impulsive intervals, and the impulsive delays is removed. Moreover, using the improved average impulsive delay (AID), a relaxed FES criterion for nonlinear CFODSs with DIs is derived. Furthermore, as an application of the obtained theoretical results, the fractional exponential synchronization of CFODINNs with DIs is studied. Finally, simulations are given to illustrate the validity of our results, where the positive effect of impulsive delays is verified.