The major goal of this work is investigating sufficient conditions for the existence and uniqueness of solutions for implicit impulsive coupled system of φ-Hilfer fractional differential equations (FDEs) with instantaneous impulses and terminal conditions. First, we derive equivalent fractional integral equations of the proposed system. Next, by employing some standard fixed point theorems such as Leray–Schauder alternative and Banach, we obtain the existence and uniqueness of solutions. Further, by mathematical analysis technique we investigate the Ulam–Hyers (UH) and generalized UH (GUH) stability of solutions. Finally, we provide a pertinent example to corroborate the results obtained.

中文翻译：

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基于φ-Hilfer分数算子的隐式脉冲耦合系统的一些性质

这项工作的主要目标是研究具有瞬时脉冲和终端条件的 φ-Hilfer 分数阶微分方程 (FDE) 的隐式脉冲耦合系统解的存在性和唯一性的充分条件。首先，我们推导出所提出系统的等效分数积分方程。接下来，通过使用一些标准不动点定理，例如 Leray-Schauder 替代和 Banach，我们获得了解的存在性和唯一性。此外，通过数学分析技术，我们研究了解的 Ulam-Hyers (UH) 和广义 UH (GUH) 稳定性。最后，我们提供了一个相关的例子来证实所获得的结果。