PRACTICAL STABILITY OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS BY LYAPUNOV FUNCTIONS

被引：7

作者：

Agarwal, Ravi ^{[1
]}

Hristova, S. ^{[2
]}

O'Regan, D. ^{[3
]}

机构：

[1] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA

[2] Paisij Hilendarski Univ Plovdiv, Dept Appl Math & Modeling, Plovdiv, Bulgaria

[3] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

来源：

DIFFERENTIAL EQUATIONS & APPLICATIONS | 2016年 / 8卷 / 01期

关键词：

practical stability; strongly practical stability; Lyapunov functions; Caputo derivatives; fractional differential equations;

D O I：

10.7153/dea-08-04

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The practical stability of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov like function along the given fractional differential equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for practical stability, practical quasi stability, strongly practical stability of the zero solution and the corresponding uniform types of practical stability are established.

引用

页码：53 / 68

页数：16

共 28 条

[1]

Agarwal R., APPL MATH IN PRESS

[2] Lyapunov functions for fractional order systems [J].

Aguila-Camacho, Norelys ;

Duarte-Mermoud, Manuel A. ;

Gallegos, Javier A. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (09) :2951-2957

[3] Practical stability of the solutions of impulsive systems of differential-difference equations via the method of comparison and some applications to population dynamics [J].

Bainov, DD ;

Dishliev, AB ;

Stamova, IM .

ANZIAM JOURNAL, 2002, 43 :525-539

[4] On the global existence of solutions to a class of fractional differential equations [J].

Baleanu, Dumitru ;

Mustafa, Octavian G. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (05) :1835-1841

[5]

Bernfeld SR, 1980, TOHOKU MATH J, V32, P607, DOI DOI 10.2748/TMJ/1178229544

[6]

Das S., 2011, FUNCT FRACT CALC 2

[7] Variational Lyapunov method for fractional differential equations [J].

Devi, J. Vasundhara ;

Mc Rae, F. A. ;

Drici, Z. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (10) :2982-2989

[8]

Diethelm K., 2010, ANAL FRACTIONAL DIFF

[9] Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems [J].

Duarte-Mermoud, Manuel A. ;

Aguila-Camacho, Norelys ;

Gallegos, Javier A. ;

Castro-Linares, Rafael .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 22 (1-3) :650-659

[10]

Henderson J., 2010, COMMUN APPL ANAL, V14, P515

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