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PreprintCC BY 4.0arXiv

Stability of Magnetizable Piezoelectric Beam Systems with Two Fractional Infinite Memory Terms

  • Jun Zhou
  • Linfeng Duan
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Abstract

In this paper, we investigate a class of magnetizable piezoelectric beam systems with two fractional infinite memory terms, whose fractional orders are denoted by θ1, θ2 ∈ [0,1]. By introducing the Dafermos history variable, we construct an augmented state space and reformulate the system as an abstract evolution equation. The well-posedness of the system is established via semigroup theory. Through a frequency-domain analysis, we characterize the asymptotic behavior of the solutions. We show that the system is exponentially stable if θ1 = θ2 = 1, and is polynomially stable in all other cases, with the explicit decay rate t−1/(2−2θ0), where θ0 = min{θ1, θ2}. Furthermore, the optimality of the obtained decay rate is verified.

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Cite

BibTeXRIS
BibTeX
@misc{zhou2026stability,
  title = {{Stability of Magnetizable Piezoelectric Beam Systems with Two Fractional Infinite Memory Terms}},
  author = {Jun Zhou and Linfeng Duan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06049},
  eprint = {2609.06049},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06049},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stability of Magnetizable Piezoelectric Beam Systems with Two Fractional Infinite Memory Terms
AU  - Jun Zhou
AU  - Linfeng Duan
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.06049
UR  - https://arxiv.org/abs/2609.06049
AB  - In this paper, we investigate a class of magnetizable piezoelectric beam systems with two fractional infinite memory terms, whose fractional orders are denoted by θ_1, θ_2 ∈ [0,1]. By introducing the Dafermos history variable, we construct an augmented state space and reformulate the system as an abstract evolution equation. The well-posedness of the system is established via semigroup theory. Through a frequency-domain analysis, we characterize the asymptotic behavior of the solutions. We show that the system is exponentially stable if θ_1 = θ_2 = 1, and is polynomially stable in all other cases, with the explicit decay rate t^−1/(2−2θ_0), where θ_0 = min{θ_1, θ_2}. Furthermore, the optimality of the obtained decay rate is verified.
ER  -