THEORETICAL AND NUMERICAL STABILITY OF THE BRESSE SYSTEM: EXPLORING FRACTIONAL DAMPING THROUGH TRADITIONAL AND NEURAL NETWORK APPROACHES

This paper investigates the theoretical and numerical stability of the one-dimensional Bresse system with fractional damping terms in a bounded domain. We first establish the well-posedness of the system. Using the frequency domain approach and a theorem by Borichev and Tomilov, we derive the polynomial decay rate of the system. To validate these theoretical results, we propose a numerical scheme and compare its performance with the Fractional Physics-Informed Neural Network (fPINN). The comparative analysis highlights the effectiveness of traditional numerical methods and fPINNs in capturing the decay rate, offering new insights into the advancement of computational techniques for complex physical systems.