Fractional averaging theory for discrete fractional-order system with impulses

Peiguang Wang; Xiang Liu; Douglas R Anderson

doi:10.1063/5.0181121

Fractional averaging theory for discrete fractional-order system with impulses

Chaos. 2024 Jan 1;34(1):013128. doi: 10.1063/5.0181121.

Authors

Peiguang Wang¹, Xiang Liu², Douglas R Anderson³

Affiliations

¹ School of Mathematics and Information Science, Hebei University, Baoding 071002, China.
² School of Mathematical Sciences, Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang 050024, China.
³ Department of Mathematics, Concordia College, Moorhead, MN 56562, USA.

PMID: 38252781
DOI: 10.1063/5.0181121

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.