We apply the noncompactness measure by Mawhin to establish sufficient conditions for the existence and uniqueness (EU) of solution to a nonlinear Cauchy problem. The aforesaid problem is investigated under impulsive and nonlinear integral boundary conditions. Further, the problem under consideration contains Caputo-type fractional-order derivative while two different kinds of delay are also involved. After establishing the existence results, we derive some adequate results for the stability analysis of Hyers–Ulam (HU) type. Here, it should be kept in mind that the proposed tools can reduce the strong compact condition by weaker compactness. For justification, we provide some examples also.

我们应用 Mawhin 的非紧凑性度量来为非线性柯西问题的解的存在性和唯一性 (EU) 建立充分条件。上述问题是在脉冲和非线性积分边界条件下研究的。此外，所考虑的问题包含 Caputo 型分数阶导数，同时还涉及两种不同类型的延迟。在建立存在性结果后，我们推导出一些足够的结果用于 Hyers-Ulam (HU) 型的稳定性分析。在这里，应该记住，所提出的工具可以通过较弱的紧凑性来减少强紧凑条件。为了说明理由，我们还提供了一些示例。