论文标题
对非均匀分数平面系统解决方案的渐近行为
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems
论文作者
论文摘要
本文致力于研究非固定分数平面系统。我们的贡献是为非平凡的解决方案的全球吸引力提供足够的条件，以使分数不均匀的线性平面系统以及平衡点对分数非线性平面系统的平衡点的Mittag-Leffler稳定性。为了实现这些目标，我们的方法如下。首先，基于凯奇（Cauchy）在复杂分析中的论点原理，我们为线性系统的渐近稳定性获得了各种明确的条件，其系数矩阵是恒定的。其次，通过使用Hankel型轮廓，我们得出了一些特殊功能的重要估计值，这些功能是由溶液对不均匀线性系统的常数公式的变化而产生的。然后，通过提出新的加权规范与Banach固定点为适当的BANACH空间结合使用，我们得到了理想的结论。最后，提供了数值示例，以说明主要理论结果的效果。
This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar systems and for the Mittag-Leffler stability of an equilibrium point to fractional order nonlinear planar systems. To achieve these goals, our approach is as follows. Firstly, based on Cauchy's argument principle in complex analysis, we obtain various explicit sufficient conditions for the asymptotic stability of linear systems whose coefficient matrices are constant. Secondly, by using Hankel type contours, we derive some important estimates of special functions arising from a variation of constants formula of solutions to inhomogeneous linear systems. Then, by proposing new weighted norms combined with the Banach fixed point theorem for appropriate Banach spaces, we get the desired conclusions. Finally, numerical examples are provided to illustrate the effect of the main theoretical results.
