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This paper provides a new proof of the existence and uniqueness of the solution for a nonlinear boundary value problem {right leftarray(1+δy)y′′+2x(1+γy)y′array=0,0

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<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>

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