In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, we define in an appropriate way initial conditions which are deeply connected with the fractional derivative used. We introduce an appropriate generalization of practical stability which we call practical stability in time. Several sufficient conditions for practical stability in time are obtained using Lyapunov functions and the modified Razumikhin technique. Two types of derivatives of Lyapunov functions are used. Some examples are given to illustrate the introduced definitions and results.

中文翻译：

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Riemann-Liouville延迟分数阶微分方程的实用稳定性

在本文中，我们研究了带时滞的非线性Riemann-Liouville分数阶微分方程组。首先，我们以适当的方式定义与所使用的分数导数密切相关的初始条件。我们介绍了实用稳定性的适当概括，我们将其及时称为实用稳定性。使用Lyapunov函数和改进的Razumikhin技术，可以获得几个实用的时间稳定性充分条件。使用李雅普诺夫函数的两种类型的导数。给出了一些示例来说明引入的定义和结果。