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Stability analysis of impulsive fractional difference equations

  • Guo–Cheng Wu EMAIL logo and Dumitru Baleanu
Published/Copyright: June 9, 2018

Abstract

We revisit motivation of the fractional difference equations and some recent applications to image encryption. Then stability of impulsive fractional difference equations is investigated in this paper. The fractional sum equation is considered and impulsive effects are introduced into discrete fractional calculus. A class of impulsive fractional difference equations are proposed. A discrete comparison principle is given and asymptotic stability of nonlinear fractional difference equation are discussed. Finally, an impulsive Mittag–Leffler stability is defined. The numerical result is provided to support the analysis.

Acknowledgments

This study was financially supported by Sichuan Science and Technology Support Program (Grant No. 2018JY0120) and China Postdoctoral Science Foundation (Grant No. 2016M602632).

We thank Prof. Fu-Lai Chen and Dr. Chao Wang for helpful discussion and suggestion, as well as to the referees for interesting comments and remarks.

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Received: 2017-12-28
Published Online: 2018-6-9
Published in Print: 2018-4-25

© 2018 Diogenes Co., Sofia

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