Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays-Reference-Cited by-同舟云学术

Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays

Published:2019-05-21 Issue:3 Volume:69 Page:583-598
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Agarwal Ravi¹²,Hristova Snezhana³,O’Regan Donal⁴

Affiliation:

1. Department of Mathematics , Texas A&M University-Kingsville , Kingsville , TX 7836349 , USA

2. Distinguished University Professor of Mathematics , Florida Institute of Technology , Melbourne , FL 32901 , USA

3. Department of Applied Mathematics and Modeling , Plovdiv University , Plovdiv , Bulgaria

4. School of Mathematics, Statistics and Applied Mathematics , National University of Ireland , Galway , Ireland

Abstract

Abstract Caputo fractional delay differential equations with non-instantaneous impulses are studied. Initially a brief overview of the basic two approaches in the interpretation of solutions is given. A generalization of Mittag-Leffler stability with respect to non-instantaneous impulses is given and sufficient conditions are obtained. Lyapunov functions and the Razumikhin technique will be applied and appropriate derivatives among the studied fractional equations is defined and applied. Examples are given to illustrate our results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0249/pdf

Reference31 articles.

1. Abbas, S.—Benchohra, M.: Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses, Math. Slovaca 67(4) (2017), 875–894.

2. Agarwal, Ravi—O’regan, D.—Hristova, S.: Stability by Lyapunov functions of nonlinear differential equations with non-instantaneous impulses, J. Appl. Math. Comput. 53(2) (2015), 147–168.

3. Agarwal, R.—Hristova, S.—O’regan, D.: A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations, Fract. Calc. Appl. Anal. 19(2) (2016), 290–318.

4. Anguraj, A.—Kanjanadevi, S.: Non-instantaneous impulsive fractional neutral differential equations with state-dependent delay, Progr. Fract. Differ. Appl. 3(3) (2017), 207–218.

5. BAI, L.—Nieto J. J.: Variational approach to differential equations with not instantaneous impulses, Appl. Math. Lett. 73 (2017), 44–48.

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