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 50 条

[41] STABILITY RESULTS OF NEUTRAL FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MULTI CAPUTO FRACTIONAL DERIVATIVES
Wang, Qi
Xie, Chenxi
Deng, Qianqian
Hu, Yuting
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2024, 17 (03): : 1347 - 1365
[42] Strict Stability of Fractional Differential Equations with a Caputo Fractional Derivative with Respect to Another Function
Agarwal, Ravi P.
Hristova, Snezhana
O'Regan, Donal
MATHEMATICS, 2025, 13 (03)
[43] Stability for Caputo Fractional Differential Systems
Choi, Sung Kyu
Kang, Bowon
Koo, Namjip
ABSTRACT AND APPLIED ANALYSIS, 2014,
[44] Solution Stability Conditions for Differential Equations with Nonmonotone Lyapunov Functions
L. B. Knyazhishche
Differential Equations, 2021, 57 : 165 - 172
[45] Solution Stability Conditions for Differential Equations with Nonmonotone Lyapunov Functions
Knyazhishche, L. B.
DIFFERENTIAL EQUATIONS, 2021, 57 (02) : 165 - 172
[46] Lyapunov functions and convergence to steady state for differential equations of fractional order
Vergara, Vicente
Zacher, Rico
MATHEMATISCHE ZEITSCHRIFT, 2008, 259 (02) : 287 - 309
[47] Lyapunov functions and convergence to steady state for differential equations of fractional order
Vicente Vergara
Rico Zacher
Mathematische Zeitschrift, 2008, 259 : 287 - 309
[48] Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions
A. A. Kilbas
S. A. Marzan
Differential Equations, 2005, 41 : 84 - 89
[49] Nonlinear differential equations with the caputo fractional derivative in the space of continuously differentiable functions
Kilbas, AA
Marzan, SA
DIFFERENTIAL EQUATIONS, 2005, 41 (01) : 84 - 89
[50] Exponential form for Lyapunov function and stability analysis of the fractional differential equations
Sene, Ndolane
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2018, 18 (04): : 388 - 397

← 1 2 3 4 5 →