This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

中文翻译：

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广义反周期边界条件解脉冲分数缩放弓微分方程

这项研究调查了与缩放仪结合的脉冲分数阶微分方程的解。这项工作扩展并改进了脉冲分数阶微分方程的一些结果。提出了具有更一般的反周期边界条件的脉冲分数缩放仪的微分方程。通过使用Banach和Krasnoselskii的众所周知的不动点定理，确定了所提出问题的解的存在性和唯一性。此外，给出了两个例子来支持我们的理论分析。