Fractional averaging theory for discrete fractional-order system with impulses-Reference-Cited by-同舟云学术

Fractional averaging theory for discrete fractional-order system with impulses

Published:2024-01-01 Issue:1 Volume:34 Page:
ISSN:1054-1500
Container-title:Chaos: An Interdisciplinary Journal of Nonlinear Science
language:en
Short-container-title:

Author:

Wang Peiguang¹^ORCID,Liu Xiang²^ORCID,Anderson Douglas R.³^ORCID

Affiliation:

1. School of Mathematics and Information Science, Hebei University 1 , Baoding 071002, China

2. School of Mathematical Sciences, Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University 2 , Shijiazhuang 050024, China

3. Department of Mathematics, Concordia College 3 , Moorhead, MN 56562, USA

Abstract

In this paper, we improve the averaging theory on both finite and infinite time intervals for discrete fractional-order systems with impulses. By employing new techniques, generalized impulsive discrete fractional-order Gronwall inequality is introduced. In addition, the closeness of solutions for the discrete fractional-order systems with impulses and the averaged discrete fractional-order systems with impulses is derived. Finally, three examples are provided to illustrate the efficiency of our main results.

Funder

National Natural Science Foundation of China

Hebei Provincial Key Research Projects

the Youth Top Talent Project of Hebei Education Department

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0181121/18701373/013128_1_5.0181121.pdf

Reference26 articles.

1. Averaging analysis for discrete time and sampled adaptive systems;IEEE Trans. Circuits Syst.,1988

2. Averaging theory for delay difference equations with time-varying delays;SIAM J. Appl. Math.,1999

3. Fundamental theorems of averaging for functional differential equations;J. Differ. Equ.,1999