A fractional order problem arising in porous media is considered. Well-posedness as well as stability are discussed. Mittag-Leffler stability is proved in case of a strong fractional damping in the displacement component and a fractional frictional one in the volume fraction component. This extends an existing result from the integer-order (second-order) case to the non-integer case. In the absence of the fractional damping in the volume fraction component, it is shown a convergence to zero and a Lyapunov uniform stability.

中文翻译：

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多孔介质中出现的问题的 Mittag-Leffler 稳定性和 Lyapunov 稳定性

考虑多孔介质中出现的分数阶问题。讨论了适定性和稳定性。 Mittag-Leffler 稳定性在位移分量中存在强分数阻尼和体积分数分量中存在分数摩擦阻尼的情况下得到了证明。这将现有结果从整数阶（二阶）情况扩展到非整数情况。在体积分数分量中不存在分数阻尼的情况下，表现出收敛到零和李亚普诺夫均匀稳定性。