Hybrid Fractional-Neural Multi-Agent Systems with Neutral Delay: Dynamical Stability and Predictive AI Modelling

This paper investigates the dynamical behavior of hybrid fractional-neural multi-agent systems with neutral delays modelled using Caputo fractional derivatives to capture non-local memory effects in neural dynamics. The proposed framework establishes positivity, boundedness, equilibrium existence, and stability using Lyapunov functionals, fractional Grönwall inequalities, and Mittag-Leffler stability theory. Positivity guarantees non-negative solutions for biological and computational interpretations, while boundedness ensures finite state trajectories. Existence and uniqueness of equilibrium points are derived under Lipschitz conditions. A unified hybrid fractional-neural predictive architecture integrates fractional dynamic processing, deep neural feature extraction, time-delay embedding, and adaptive feedback control. The associated predictive control procedure is formalized in Algorithm where fractional operators, neural mappings, and delay interactions are fused through a coupled transformation to generate predictive outputs and adaptive control signals. Lyapunov-based adaptation laws ensure asymptotic convergence and closed-loop stability. Simulation results for fractional orders [Formula: see text], and demonstrate consistent convergence and accurate AI-based parameter prediction. The proposed methodology contributes to the stability theory of fractional-order systems and enhances predictive modeling capability for complex multi-agent neural networks.