Stability of Caputo fractional differential equations by Lyapunov functions

Ravi P. Agarwal; Donal O'Regan; Snezhana Hristova

Applications of Mathematics (2015)

  • Volume: 60, Issue: 6, page 653-676
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Agarwal, Ravi P., O'Regan, Donal, and Hristova, Snezhana. "Stability of Caputo fractional differential equations by Lyapunov functions." Applications of Mathematics 60.6 (2015): 653-676. <http://eudml.org/doc/271818>.

@article{Agarwal2015,
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.},
author = {Agarwal, Ravi P., O'Regan, Donal, Hristova, Snezhana},
journal = {Applications of Mathematics},
keywords = {stability; Caputo derivative; Lyapunov function; fractional differential equation; stability; Caputo derivative; Lyapunov function; fractional differential equation},
language = {eng},
number = {6},
pages = {653-676},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability of Caputo fractional differential equations by Lyapunov functions},
url = {http://eudml.org/doc/271818},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Agarwal, Ravi P.
AU - O'Regan, Donal
AU - Hristova, Snezhana
TI - Stability of Caputo fractional differential equations by Lyapunov functions
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 6
SP - 653
EP - 676
AB - 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.
LA - eng
KW - stability; Caputo derivative; Lyapunov function; fractional differential equation; stability; Caputo derivative; Lyapunov function; fractional differential equation
UR - http://eudml.org/doc/271818
ER -

References

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