Abstract In this paper, we mainly consider the existence and Hyers-Ulam stability of solutions for a class of fractional differential equations involving time-varying delays and non-instantaneous impulses. By the Krasnoselskii’s fixed point theorem, we present the new constructive existence results for the addressed equation. In addition, we deduce that the equations have Hyers-Ulam stable solutions by utilizing generalized Grönwall’s inequality. Some results in this literature are new and improve some early conclusions.

中文翻译：

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一类具有非瞬时脉冲的分数阶时滞微分方程的存在性和Hyers-Ulam稳定性结果

摘要 本文主要考虑一类包含时变时滞和非瞬时脉冲的分数阶微分方程解的存在性和Hyers-Ulam稳定性。通过Krasnoselskii不动点定理，我们给出了求解方程的新的构造存在结果。此外，我们利用广义Grönwall 不等式推导出方程具有Hyers-Ulam 稳定解。该文献中的一些结果是新的，并改进了一些早期结论。