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In this paper, we consider a thermo-elastic system of type Ⅱ with fractional boundary damping. First, using a general criteria of Maryati et al., we prove the lack of exponential stable of the system under feedback control of fractional order 0<θ<1. Next, we obtain a polynomial decay rate of the above system using frequency domain approach combined with a detailed spectral analysis.
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Ge et al. (2024) studied this question.
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