Existence and Stability Analysis of Classical and Fractional‐Order Generalized Brusselator Reaction‐Diffusion System

The present work is devoted to establishing existence results and examining the stability properties of solutions associated with a generalized Brusselator reaction–diffusion system in both the classical and fractional‐order settings. The corresponding ODE and PDE formulations are considered to establish the global existence of solutions in the classical framework through a suitable Lyapunov functional, while local existence is addressed for the fractional‐order system. We further obtain sufficient criteria guaranteeing local asymptotic stability of the resulting solutions. As an application of the theoretical results, the classical Brusselator reaction–diffusion model is recovered as a special case of the generalized system, and numerical simulations are carried out to examine the behavior of its solutions under the derived conditions.