Abstract We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's invariance principle we show that the system is strongly stable. Then, based on a resolvent approach we show a luck of uniform stabilization. Next, using multiplier techniques combined with the frequency domain method, we shall give a polynomial stabilization result under some consideration on the stabilization of an auxiliary dissipating system. Finally, we give some applications to the wave equation.

中文翻译：

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一类演化系统的分数反馈镇定

摘要 我们研究了一类具有分数阻尼的演化系统的镇定问题。在将方程写为增强系统后，我们首先在本文中证明问题是适定的。其次，使用 LaSalle 不变性原理，我们证明系统是强稳定的。然后，基于解析方法，我们展示了均匀稳定的运气。接下来，使用乘法器技术结合频域方法，我们将在考虑辅助耗散系统的稳定性的情况下给出多项式稳定结果。最后，我们给出了波动方程的一些应用。