Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and fractional-order-independent stability and instability properties are fully characterised, in terms of the main diagonal elements of the systems’ matrix, as well as its determinant.

中文翻译：

---

分数阶微分方程的二维线性自治多阶系统的精确稳定性和不稳定性区域

探索了具有Caputo导数的分数阶微分方程的线性二维自治系统的渐近稳定性和不稳定性的充要条件。根据系统矩阵的主要对角元素及其行列式，充分表征了分数阶相关和分数阶独立的稳定性和不稳定性。