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Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses

  • Danfeng Luo and Zhiguo Luo EMAIL logo
From the journal Mathematica Slovaca

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.


This work was supported by the National Natural Science Foundation of China (No.11471109).


  1. (Communicated by Michal Fečkan)

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Received: 2019-11-06
Accepted: 2020-01-12
Published Online: 2020-09-27
Published in Print: 2020-10-27

© 2020 Mathematical Institute Slovak Academy of Sciences

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