In this paper, we introduce a new class of fractional impulsive systems of functions with respect to another function in which the order of the fractional derivative and the kernel function is associated with the impulses. We derive the solution representation, investigate the existence, and uniqueness of solutions of such a Caputo-type fractional impulsive system. Besides, the data dependence of the system is discussed. Our arguments are based on some classical fixed-point styles. Three various examples are provided to illustrate the validation of the main results. An open problem is presented in the conclusion section to bring the attention to a more general setting.

在本文中，我们介绍了一类新的分数阶脉冲函数系统，相对于另一个函数，其中分数阶导数和核函数的阶数与脉冲相关。我们推导出解表示，研究这种 Caputo 型分数脉冲系统解的存在性和唯一性。此外，还讨论了系统的数据依赖性。我们的论点是基于一些经典的定点风格。提供了三个不同的例子来说明主要结果的验证。结论部分提出了一个悬而未决的问题，以引起人们对更一般情况的关注。