This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).

中文翻译：

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Caputo分式边界条件下非局部内隐脉冲问题的数学分析。

本文与非局部Caputo分数阶边界条件（NCFBC）下的脉冲分数阶微分方程（IFODE）的数学分析框架相关。通过使用Schaefer和Banach的不动点定理，我们分析了所考虑问题的存在性和唯一性结果。此外，我们利用稳定性理论来介绍拟议方案的Hyers-Ulam，广义Hyers-Ulam，Hyers-Ulam-Rassias和广义Hyers-Ulam-Rassias稳定性结果。最后，提供了一些应用程序来演示概念和结果。整个分析是通过使用Caputo分数导数（CFD）进行的。