Some stability properties related to initial time difference for Caputo fractional differential equations-Reference-Cited by-同舟云学术

Some stability properties related to initial time difference for Caputo fractional differential equations

Published:2018-02-01 Issue:1 Volume:21 Page:72-93
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Agarwal Ravi¹,Hristova Snezhana²,O’Regan Donal³

Affiliation:

1. Department of Mathematics , Texas A&M University-Kingsville , Kingsville , TX 78363 , Usa

2. Department of Applied Mathematics , University of Plovdiv Paisii Hilendarski , Plovdiv , Bulgaria

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

Abstract

Abstract Lipschitz stability and Mittag-Leffler stability with initial time difference for nonlinear nonautonomous Caputo fractional differential equation are defined and studied using Lyapunov like functions. Some sufficient conditions are obtained. The fractional order extension of comparison principles via scalar fractional differential equations with a parameter is employed. The relation between both types of stability is discussed theoretically and it is illustrated with examples.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2018-0005/pdf

Reference24 articles.

1. S. Abbas, M. Benchohra, M.A. Darwish New stabilty results for partial fractional differential inclusions with not instantaneous impulses. Frac. Calc. Appl. Anal. 18, No 1 (2015), 172–191; 10.1515/fca-2015-0012; https://www.degruyter.com/view/j/fca.2015.18.issue-1/issue-files/fca.2015.18.issue-1.xml.

2. R. Agarwal, S. Hristova, D.O.Regan, Stability with respect to initial time difference for generalized delay differential equations. Electr. J. Diff. Eq. 49 (2015), 1–19.

3. R. Agarwal, S. Hristova, D. O’Regan, A survey of Lyapunov functions, stability and impulsive Caputo fractional differetial equations. Frac. Calc. Appl. Anal. 19, No 2 (2016), 290–318; 10.1515/fca-2016-0017; https://www.degruyter.com/view/j/fca.2016.19.issue-2/issue-files/fca.2016.19.issue-2.xml.

4. R.P. Agarwal, D. O’Regan, S. Hristova, Stability of Caputo fractional differential equations by Lyapunov’s functions. Appl. Math. 60, No 6 (2015), 653–676.

5. R.P. Agarwal, D. O’Regan, S. Hristova, M. Cicek, Practical stability with respect to initial time difference for Caputo fractional differential equations. Commun. Nonl. Sci. Numer. Simul. 42 (2017), 106–120.

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