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Positivity and stability of mixed fractional‐order systems with unbounded delays: Necessary and sufficient conditions
Authors:Hoang The Tuan  Hieu Trinh  James Lam
Abstract: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.
Keywords:asymptotic stability  fractional differential equations  linear mixed fractional‐order systems  positive systems  time‐varying delays
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