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Mathematics 2019, 7(4), 331; https://doi.org/10.3390/math7040331

Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

1 and 1,2,*
1
Department of Mathematics, Guizhou University, Guiyang 550025, China
2
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
*
Author to whom correspondence should be addressed.
Received: 19 February 2019 / Revised: 17 March 2019 / Accepted: 28 March 2019 / Published: 4 April 2019
PDF [284 KB, uploaded 4 April 2019]

Abstract

This paper gives continuous dependence results for solutions of integer and fractional order, non-instantaneous impulsive differential equations with random impulse and junction points. The notion of the continuous dependence of solutions of these equations on the initial point is introduced. We prove some sufficient conditions that ensure the solutions to perturbed problems have a continuous dependence. Finally, we use numerical examples to demonstrate the obtained theoretical results.
Keywords: non-instantaneous impulsive equations; random impulsive and junction points; continuous dependence non-instantaneous impulsive equations; random impulsive and junction points; continuous dependence
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Chen, Y.; Wang, J. Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points. Mathematics 2019, 7, 331.

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