This article provides a comprehensive study on quantitative properties of linear mixed fractional‐order systems with multiple time‐varying delays. The delays can be bounded or unbounded. We first obtain a result on existence and uniqueness of solutions to these systems. Then, we prove a necessary and sufficient condition for their positivity. Finally, we provide a necessary and sufficient criterion to characterize asymptotic stability of positive linear mixed fractional‐order systems with multiple time‐varying delays.

中文翻译：

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具有无限延迟的混合分数阶系统的正性和稳定性：必要条件和充分条件

本文对具有多个时变时滞的线性混合分数阶系统的定量性质进行了全面的研究。延迟可以是有界的或无界的。我们首先获得关于这些系统解决方案的存在性和唯一性的结果。然后，我们证明了它们的积极性的充要条件。最后，我们提供了一个必要和充分的准则，以刻画具有多个时变时滞的正线性混合分数阶系统的渐近稳定性。