In this paper, we give a systematic analysis for solutions to two-term fractional differential equations. Our main contribution is in Section 5. In this section we have shown the global attractiveness, the Mittag-Leffler stability and the local attractiveness of solutions to some classes of two-term fractional differential equations. To do these, our approach is combining Cauchy’s argument principle in complex analysis (to obtain an explicit necessary and sufficient condition for the asymptotic stability of linear equations), the Hankel type contour (to estimate the decay rate of special functions arising in the elementary solutions) and a linearization method developed recently for fractional-order differential equations (to prove the Mittag-Leffler stability of the trivial solution to nonlinear equations and the local attractivity of the origin for the inhomogeneous nonlinear case). Numerical simulations are finally presented to confirm the theoretical findings.

在本文中，我们对二项分数阶微分方程的解进行了系统的分析。我们的主要贡献在第 5 节中。在本节中，我们展示了某些类别的二项分数微分方程解的全局吸引力、Mittag-Leffler 稳定性和局部吸引力。为此，我们的方法是在复分析中结合柯西论证原理（以获得线性方程渐近稳定性的显式充要条件），Hankel 型等值线（用于估计基本解中出现的特殊函数的衰减率）和最近为分数阶微分方程开发的线性化方法（用于证明非线性方程的平凡解的 Mittag-Leffler 稳定性和局部吸引力非齐次非线性情况的起源）。最后提出数值模拟以证实理论发现。