On the asymptotic stability of a Bresse system with two fractional damping terms: Theoretical and numerical analysis

Abstract

<p style='text-indent:20px;'>The aim of this work is to investigate the asymptotic stability of a viscoelastic Bresse system in one dimensional bounded domain. In this context, we introduce two internal damping terms expressed using the generalized Caputo fractional derivative. By adopting a diffusive representation, we show the well-posedness of the proposed system and we prove some decay results. In order to validate the theoretical findings, we implement a finite difference method and we conduct intensive numerical simulations. Moreover, we provide some insights on the convergence of the elaborated numerical scheme.</p>