Stability Analysis of Impulsive Fractional Difference Equations

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 fract...

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Bibliographic Details
Published in:Fractional calculus & applied analysis Vol. 21; no. 2; pp. 354 - 375
Main Authors: Wu, Guo–Cheng, Baleanu, Dumitru
Format: Journal Article
Language:English
Published: Warsaw Versita 01.04.2018
De Gruyter
Nature Publishing Group
Subjects:
Abstract Harmonic Analysis
Analysis
asymptotic stability
comparison principle
Difference equations
discrete–time control
Encryption
Fractional calculus
Functional Analysis
impulsive fractional difference equations
Integral Transforms
Mathematical analysis
Mathematics
Mittag–Leffler stability
Operational Calculus
Primary 34A08
Research Paper
Secondary 39A30, 34K20, 34A37
Stability analysis
Primary 34A08
impulsive fractional difference equations
34A37
Mittag–Leffler stability
Secondary 39A30
asymptotic stability
34K20
comparison principle
discrete–time control
ISSN:1311-0454, 1314-2224
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2018-0021