A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations

DOI10.1515/fca-2016-0017zbMath1343.34006OpenAlexW2425580862MaRDI QIDQ281420

Donal O'Regan, Ravi P. Agarwal, Snezhana G. Hristova

Publication date: 11 May 2016

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2016-0017

zbMATH Keywords

stabilityimpulsesLyapunov functionsfractional differential equationsCaputo derivativeCaputo population model

Mathematics Subject Classification ID

Ordinary differential equations with impulses (34A37) Fractional derivatives and integrals (26A33) Stability of solutions to ordinary differential equations (34D20) Fractional ordinary differential equations (34A08)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global stability of impulsive fractional differential equations
• On the concept of general solution for impulsive differential equations of fractional order \(q (0, 1)\)
• Stability analysis of impulsive fractional-order systems by vector comparison principle
• Variational Lyapunov method for fractional differential equations
• On recent developments in the theory of boundary value problems for impulsive fractional differential equations
• On the concept and existence of solution for impulsive fractional differential equations
• Ulam's type stability of impulsive ordinary differential equations
• On the natural solution of an impulsive fractional differential equation of order \(q\in (1,2)\)
• Nonlocal boundary value problem for impulsive differential equations of fractional order
• Fractional differential equations and Lyapunov functionals
• Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order
• A Lyapunov approach to the stability of fractional differential equations
• Asymptotical stability of nonlinear fractional differential system with Caputo derivative
• Stability of Caputo fractional differential equations by Lyapunov functions.
• Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems
• Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations
• Mittag-Leffler stability of fractional order nonlinear dynamic systems
• A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
• Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
• On the global existence of solutions to a class of fractional differential equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Fractional quantum mechanics and Lévy path integrals
• Lyapunov functions and strict stability of Caputo fractional differential equations
• Comments on the concept of existence of solution for impulsive fractional differential equations
• Lyapunov functions for fractional order systems
• Response to ``Comments on the concept of existence of solution for impulsive fractional differential equations
• Multiple solutions to boundary value problem for impulsive fractional differential equations
• Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay
• Decay integral solutions for a class of impulsive fractional differential equations in Banach spaces
• Stability analysis for nonlinear fractional-order systems based on comparison principle
• Lyapunov stability theorem about fractional system without and with delay
• Practical Stability of Caputo fractional differential equations by Lyapunov functions
• Existence of solutions to boundary value problem for impulsive fractional differential equations
• Functional Fractional Calculus
• On some impulsive fractional differential equations in Banach spaces
• Impulsive fractional differential equations in Banach spaces
• Existence of solutions of abstract fractional impulsive semilinear evolution equations

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