Exponential stability of impulsive fractional-order neural networks with time-varying delays and reaction-diffusion terms

This paper investigates the exponential stability of a class of impulsive fractional-order neural networks incorporating time-varying delays and reaction-diffusion terms. The considered model captures both instantaneous and delayed impulsive effects, providing a more realistic framework for describing complex impulsive dynamics in neural systems. Motivated by the limitations in existing studies on asymptotic stability, we establish a novel theoretical framework for exponential stability analysis fractional-order neural networks with delays, impulsive effects, and spatial diffusion. By employing Lyapunov functionals and linear matrix inequalities, we derive sufficient conditions that ensure global exponential stability of the equilibrium point, with explicit convergence rates. These conditions unify and generalise prior results for delay-free or integer-order systems, exhibiting reduced conservativeness and applicability to engineering contexts. Numerical simulations validate the obtained results, demonstrating rapid exponential convergence of system states despite impulsive perturbations. The proposed framework provides an efficient tool for analyzing the stability of fractional-order neural networks with complex spatiotemporal dynamics.