In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

中文翻译：

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具反周期边界条件的耦合脉冲分数阶受电弓微分方程解的存在唯一性

在本文中，我们研究了带有瞬时脉冲的耦合比例缩放缩放微分方程的解。这项工作改进了一些现有的结果，并为分数阶微分方程理论的发展做出了贡献。我们首先提供一些将在整篇论文中使用的定义。之后，我们给出了基于Banach压缩原理和Krasnoselskii不动点定理的存在性和唯一性结果。最后一部分给出了两个例子来支持我们的研究。