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Stability of caputo fractional differential equations by lyapunov functions

Agarwal, Ravi
; 
O’Regan, Donal
; 
Hristova, Snezhana
Identifiers
http://hdl.handle.net/10379/10137
 https://doi.org/10.13025/28384
Publication Date
2015-12-01
Keywords
stability, caputo derivative, lyapunov function, fractional differential equation
Type
Article
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Citation
Agarwal, Ravi; O’Regan, Donal; Hristova, Snezhana (2015). Stability of caputo fractional differential equations by lyapunov functions. Applications of Mathematics 60 (6), 653-676
Abstract
The stability of the zero solution 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 equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based on the new definition of the derivative of Lyapunov functions and the new comparison result, are established.
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Publisher
Institute of Mathematics, Czech Academy of Sciences
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)