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>

A Novel Implementation of Krasnoselskii’s Fixed-Point Theorem to a Class of Nonlinear Neutral Differential Equations

“…Remark 4. Any solution to equation ( 31) is a solution to problem (1). Let us introduce the following hypotheses, which are assumed hereafter:…”

“…In recent years, differential equations have garnered considerable interest (cf. [1,2] and references therein). Important types of these problems include differential equations with delay.…”

“…Important types of these problems include differential equations with delay. For instance, in [1,[3][4][5][6][7][8][9][10], the authors employed a variety of techniques to determine the existence of positive periodic solutions. The uniqueness and positivity of a first-order nonlinear periodic differential equation are investigated in [11].…”

“…The remainder of this paper is organized as follows: in the next Section, we deliver the definitions and lemmas required to prove our main results. In particular, we state some Green's function properties related to the problem (1). Section 3 establishes some necessary conditions for the existence of positive solutions to our problem (1).…”

A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations

“…Numerous disciplines employ fractional analysis. The fractional differential operators Riemann-Liouville, Grunwald-Letnikov, Riesz, Hadamard, Caputo, Caputo-Fabrizio, etc., represent only some examples, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”