关于混合阶分数阶齐次合作时滞系统的Mittag-Leffler稳定性
On the Mittag-Leffler stability of mixed-order fractional homogeneous cooperative delay systems
AI总结：
本文研究多阶分数阶非线性时滞系统，证明在合作性、齐次性和保序性等结构性假设下系统的Mittag-Leffler稳定性，适用于非时滞与时滞分量齐次度不同的情况，并分析了解的收敛速度。
摘要：
本文研究一类多阶分数阶非线性时滞系统。我们的主要贡献是证明当对“向量场”施加某些结构性假设时系统的（局部或全局）Mittag-Leffler稳定性：合作性、齐次性以及在相空间正卦限上的保序性。特别地，我们的方法适用于向量场的非时滞分量与时滞分量的齐次度不同的情况。此外，我们还详细研究了解向平衡点的收敛速度。还提供了两个具体例子以说明所提出理论结果的有效性。
英文摘要：
In this paper, we study a class of multi-order fractional nonlinear delay systems. Our main contribution is to show the (local or global) Mittag-Leffler stability of systems when some structural assumptions are imposed on the "vector fields": cooperativeness, homogeneity, and order-preserving on the positive orthant of the phase space. In particular, our method is applicable to the case where the degrees of homogeneity of the non-lag and lag components of the vector field are different. In addition, we also investigate in detail the convergence rate of the solutions to the equilibrium point. Two specific examples are also provided to illustrate the validity of the proposed theoretical result.
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