Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays

Ravi Agarwal; Snezhana Hristova; Donal O’Regan

doi:10.1007/s12591-018-0434-6

Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays

Ravi Agarwal
, Snezhana Hristova
, Donal O’Regan

Mathematics

Texas A&M University-Kingsville
Florida Institute of Technology
University of Plovdiv Paisii Hilendarski

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

17 Citations (Scopus)

Abstract

The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.

Original language	English
Pages (from-to)	513-534
Number of pages	22
Journal	Differential Equations and Dynamical Systems
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s12591-018-0434-6
Publication status	Published - Jul 2022

Keywords

Caputo fractional differential equations
Fractional derivative of Lyapunov functions
Lyapunov functions
Stability

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10.1007/s12591-018-0434-6

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abstract = "The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.",

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author = "Ravi Agarwal and Snezhana Hristova and Donal O{\textquoteright}Regan",

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AU - O’Regan, Donal

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Y1 - 2022/7

N2 - The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.

AB - The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.

KW - Caputo fractional differential equations

KW - Fractional derivative of Lyapunov functions

KW - Lyapunov functions

KW - Stability

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JO - Differential Equations and Dynamical Systems

JF - Differential Equations and Dynamical Systems

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ER -

Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays

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