Electron. J. Differential Equations, Vol. 2026 (2026), No. 73, pp. 1-22.

Stabilization of a degenerate beam on an elastic foundation with axial force under fractional derivative-type delayed boundary feedback

Lanzhi Cao, Sheng-Jie Li, Shugen Chai

Abstract:
In this article, we investigate the exponential stabilization of a degenerate Euler-Bernoulli beam on an elastic foundation with axial force. The control input at the boundary features a fractional derivative-type delay. We construct a tailored Lyapunov functional, specifically designed to offset the effects of time delay and capture the intrinsic internal dynamics of the degenerate beam, thereby rigorously establishing the exponential stability of the system.

Submitted February 12, 2026. Published September 22, 2026.
Math Subject Classifications: P58J35, 53E20.
Key Words: Degenerate beam equation; elastic foundation; axial force; fractional derivative; time delay; Lyapunov functional.
DOI: 10.58997/ejde.2026.73

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Lanzhi Cao
School of Mathematics and Statistics
Shanxi University
Taiyuan 030006, China
email: caolanzhi1114@163.com
Sheng-Jie Li
School of Mathematical Sciences
Fudan University
Shanghai 200433, China
email: lishengjiebo@163.com, li_sj@fudan.edu.cn
Shugen Chai
School of Mathematics and Statistics
Shanxi University
Taiyuan, 030006, China
email: sgchai@sxu.edu.cn

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