Four Ulam type stability concepts for non-instantaneous impulsive fractional differential equations with state dependent delay are introduced. Two different approaches to the interpretation of solutions are investigated. We study the case of an unchangeable lower bound of the Caputo fractional derivative and the case of a lower bound coinciding with the point of jump for the solution. In both cases we obtain sufficient conditions for Ulam type stability. An example is also provided to illustrate both approaches.

中文翻译：

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具有状态依赖时滞的非瞬时脉冲Caputo分数阶微分方程的Ulam型稳定性

介绍了具有状态依赖时滞的非瞬时脉冲分数阶微分方程的四个Ulam型稳定性概念。研究了两种不同的解法。我们研究了Caputo分数导数的不变下界的情况，以及与解的跳跃点一致的下界的情况。在这两种情况下，我们都获得了Ulam型稳定性的充分条件。还提供了一个示例来说明这两种方法。