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

[31] Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations
Fahad, Hafiz Muhammad
Fernandez, Arran
APPLIED MATHEMATICS AND COMPUTATION, 2021, 409
[32] Mittag-Leffler Stability for Impulsive Caputo Fractional Differential Equations
Agarwal, R.
Hristova, S.
O'Regan, D.
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2021, 29 (03) : 689 - 705
[33] Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives
Brandibur, Oana
Garrappa, Roberto
Kaslik, Eva
MATHEMATICS, 2021, 9 (08)
[34] HYERS-ULAM-RASSIAS STABILITY OF κ-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS
Yao, Hui
Jin, Wenqi
Dong, Qixiang
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (05): : 2903 - 2921
[35] STABILITY ANALYSIS OF NONLINEAR UNCERTAIN FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO DERIVATIVE
Lu, Ziqiang
Zhu, Yuanguo
Lu, Qinyun
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (03)
[36] Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations
Baleanu, Dumitru
Wu, Guo-Cheng
Zeng, Sheng-Da
CHAOS SOLITONS & FRACTALS, 2017, 102 : 99 - 105
[37] Stability with respect to part of the variables of nonlinear Caputo fractional differential equations
Ben Makhlouf, Abdellatif
MATHEMATICAL COMMUNICATIONS, 2018, 23 (01) : 119 - 126
[38] On the Existence and Stability of Variable Order Caputo Type Fractional Differential Equations
Sarwar, Shahzad
FRACTAL AND FRACTIONAL, 2022, 6 (02)
[39] ULAM STABILITY AND DATA DEPENDENCE FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO DERIVATIVE
Wang, JinRong
Lv, Linli
Zhou, Yong
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2011, (63) : 1 - 10
[40] Ulam Stability for Delay Fractional Differential Equations with a Generalized Caputo Derivative
Ameen, Raad
Jarad, Fahd
Abdeljawad, Thabet
FILOMAT, 2018, 32 (15) : 5265 - 5274

← 1 2 3 4 5 →