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Discontinuity, Nonlinearity, and Complexity 13(4) (2024) 689--706 | DOI:10.5890/DNC.2024.12.009

S. Bousserhane Reda$^1$, A. Memou$^1$, A. Berkane$^1$, Kh. Zennir$^{2,3}$

$^1$ Laboratory of Differential Equations, Department of Mathematics, College of Sciences, University of Constantine, Algeria

$^2$ Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia

$^3$ Laboratoire de Math'ematiques Appliqu'ees et de Mod'elisation, Universit'e 8 Mai 1945 Guelma. B.P. 401 Guelma 24000 Alg'erie

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Abstract

Due to the lack of effective research methods, the study of fractional time-varying and boundary feedback for Lam\'e system requires special studies and the involvement of new methods, so there are few works in this direction. The paper is devoted to Lam\'e system with fractional time-varying and boundary feedback. A general description of the question of well posedness of problem, their stability, and a review of the results are given. The novelty and main contributions located in the interaction between different damping terms and show the impact of each one of them on the stability.

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