A Theoretical and Computational Study of the Fractional Brusselator System with Neural Network Validation

This work introduces the time-space fractional Brusselator (TSFB) model, a generalisation of the classical reaction-diusion system that describes autocatalytic chemical oscillations and pattern formation. The model consists of two fractional parameters, σ and η, that incorporate memory and non-local spatial eects, respectively. A complete qualitative analysis is presented, including existence, uniqueness, and UlamHyers (UH) stability. A nite dierence scheme is developed for numerical analysis. A neural network (NN) approach is employed to validate accuracy and reliability. Detailed simulations illustrate how the fractional parameters σ and η inuence the solutions behaviour in two and three dimensions. The principal novelty of this work lies in the combined application of fractional operators, a nite dierence method, and neural computing to the TSFB system, oering a unied framework for analysing complex nonlinear fractional dynamical systems.