Mittag–Leffler Stability for Impulsive Caputo Fractional Differential Equations

R. Agarwal; S. Hristova; D. O’Regan

doi:10.1007/s12591-017-0384-4

Mittag–Leffler Stability for Impulsive Caputo Fractional Differential Equations

R. Agarwal, S. Hristova, D. O’Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

9 Citations (Scopus)

Abstract

The stability properties of Caputo fractional differential equations with impulses are studied. Both types of impulses, non-instantaneous impulses as well as instantaneous impulses are considered. The two approaches in the literature for the interpretation ofsolutions of impulsive Caputo fractional differential equations are presented and discussed. A generalization of Mittag–Leffler stability with respect to both types of impulses is given.

Original language	English
Pages (from-to)	689-705
Number of pages	17
Journal	Differential Equations and Dynamical Systems
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s12591-017-0384-4
Publication status	Published - Jul 2021

Keywords

Caputo fractional derivative
Caputo fractional Dini derivative
Instantaneous impulses
Lyapunov functions
Mittag–Leffler stability
Non-instantaneous impulses

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10.1007/s12591-017-0384-4

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title = "Mittag–Leffler Stability for Impulsive Caputo Fractional Differential Equations",

abstract = "The stability properties of Caputo fractional differential equations with impulses are studied. Both types of impulses, non-instantaneous impulses as well as instantaneous impulses are considered. The two approaches in the literature for the interpretation ofsolutions of impulsive Caputo fractional differential equations are presented and discussed. A generalization of Mittag–Leffler stability with respect to both types of impulses is given.",

keywords = "Caputo fractional derivative, Caputo fractional Dini derivative, Instantaneous impulses, Lyapunov functions, Mittag–Leffler stability, Non-instantaneous impulses",

author = "R. Agarwal and S. Hristova and D. O{\textquoteright}Regan",

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AU - Agarwal, R.

AU - Hristova, S.

AU - O’Regan, D.

PY - 2021/7

Y1 - 2021/7

N2 - The stability properties of Caputo fractional differential equations with impulses are studied. Both types of impulses, non-instantaneous impulses as well as instantaneous impulses are considered. The two approaches in the literature for the interpretation ofsolutions of impulsive Caputo fractional differential equations are presented and discussed. A generalization of Mittag–Leffler stability with respect to both types of impulses is given.

AB - The stability properties of Caputo fractional differential equations with impulses are studied. Both types of impulses, non-instantaneous impulses as well as instantaneous impulses are considered. The two approaches in the literature for the interpretation ofsolutions of impulsive Caputo fractional differential equations are presented and discussed. A generalization of Mittag–Leffler stability with respect to both types of impulses is given.

KW - Caputo fractional derivative

KW - Caputo fractional Dini derivative

KW - Instantaneous impulses

KW - Lyapunov functions

KW - Mittag–Leffler stability

KW - Non-instantaneous impulses

UR - https://www.scopus.com/pages/publications/85081295335

U2 - 10.1007/s12591-017-0384-4

DO - 10.1007/s12591-017-0384-4

M3 - Article

AN - SCOPUS:85081295335

SN - 0971-3514

VL - 29

SP - 689

EP - 705

JO - Differential Equations and Dynamical Systems

JF - Differential Equations and Dynamical Systems

IS - 3

ER -

Mittag–Leffler Stability for Impulsive Caputo Fractional Differential Equations

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Keywords

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