In this manuscript, we present the existence and uniqueness of solution of first order non-linear impulsive delay dynamic systems on time scales, with the help of fixed point approach. Further, we investigate the Bielecki–Ulam–Hyers stability and Bielecki–Ulam–Hyers–Rassias stability of the proposed model. We use Grönwall’s inequality on time scales, Banach contraction principle, Picard operator and Lipschitz condition as a basic tools to develop our main results. Also, two examples are provided to illustrate the obtained results.

中文翻译：

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时间尺度上一阶非线性脉冲时滞动力系统的Bielecki–Ulam型稳定性结果

在此手稿中，我们借助定点方法介绍了时标上一阶非线性脉冲时滞动力系统解的存在性和唯一性。此外，我们研究了拟议模型的Bielecki–Ulam–Hyers稳定性和Bielecki–Ulam–Hyers–Rassias稳定性。我们使用时间尺度上的Grönwall不等式，Banach收缩原理，Picard算子和Lipschitz条件作为得出我们主要结果的基本工具。另外，提供了两个示例来说明获得的结果。