We extend the well-known Halanay inequality to the fractional-order case in presence of distributed delays and delays of neutral type (in the fractional derivative). Both the discrete and distributed neutral delays are investigated. It is proved that solutions decay toward zero in a Mittag–Leffler manner under some rather general conditions. Some large classes of kernels and examples satisfying our assumptions are provided. We apply our findings to prove Mittag–Leffler stability for solutions of fractional neutral network systems of Cohen–Grossberg type.

中文翻译：

---

一个中性分数 Halanay 不等式及其在 Cohen-Grossberg 神经网络系统中的应用

我们将众所周知的 Halanay 不等式扩展到存在分布式延迟和中性类型延迟（在分数阶导数中）的分数阶情况。研究了离散和分布式中性延迟。证明在一些相当普遍的条件下，解以 Mittag-Leffler 方式衰减到零。提供了一些满足我们假设的大类内核和示例。我们应用我们的发现来证明 Cohen-Grossberg 型分数中性网络系统解的 Mittag-Leffler 稳定性。