Acta Mathematica Scientia ( IF 1 ) Pub Date : 2021-04-19 , DOI: 10.1007/s10473-021-0310-2 Jiafa Xu , Bakhtawar Pervaiz , Akbar Zada , Syed Omar Shah
In this article, we present the existence, uniqueness, Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales, with the help of a fixed point approach. We use Grönwall’s inequality on time scales, an abstract Gröwall’s lemma and a Picard operator as basic tools to develop our main results. To overcome some difficulties, we make a variety of assumptions. At the end an example is given to demonstrate the validity of our main theoretical results.
中文翻译:
时间尺度上因果积分演化脉冲系统的稳定性分析
在本文中,我们借助于定点方法,介绍了时间尺度上的半线性非自治积分因果演化脉冲积分-时滞动力系统的存在性,唯一性,Ulam-Hyers-稳定性和Ulam-Hyers-Rassias稳定性。我们使用时间尺度上的Grönwall不等式,抽象的Gröwall引理和Picard运算符作为开发我们主要结果的基本工具。为了克服一些困难,我们做出了各种假设。最后给出一个例子说明我们的主要理论结果的正确性。