Geodesic
Stability of Caputo fractional differential equations by Lyapunov functions
Applications of Mathematics, Tome 60 (2015) no. 6, pp. 653-676

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.1007/s10492-015-0116-4
Classification : 34A08, 34A34, 34D20
Keywords: stability; Caputo derivative; Lyapunov function; fractional differential equation 
@article{10_1007_s10492_015_0116_4,
     author = {Agarwal, Ravi and O'Regan, Donal and Hristova, Snezhana},
     title = {Stability of {Caputo} fractional differential equations by {Lyapunov} functions},
     journal = {Applications of Mathematics},
     pages = {653--676},
     publisher = {mathdoc},
     volume = {60},
     number = {6},
     year = {2015},
     doi = {10.1007/s10492-015-0116-4},
     mrnumber = {3436567},
     zbl = {06537667},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0116-4/}
}
TY  - JOUR
AU  - Agarwal, Ravi
AU  - O'Regan, Donal
AU  - Hristova, Snezhana
TI  - Stability of Caputo fractional differential equations by Lyapunov functions
JO  - Applications of Mathematics
PY  - 2015
SP  - 653
EP  - 676
VL  - 60
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0116-4/
DO  - 10.1007/s10492-015-0116-4
LA  - en
ID  - 10_1007_s10492_015_0116_4
ER  - 
%0 Journal Article
%A Agarwal, Ravi
%A O'Regan, Donal
%A Hristova, Snezhana
%T Stability of Caputo fractional differential equations by Lyapunov functions
%J Applications of Mathematics
%D 2015
%P 653-676
%V 60
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0116-4/
%R 10.1007/s10492-015-0116-4
%G en
%F 10_1007_s10492_015_0116_4
Agarwal, Ravi; O'Regan, Donal; Hristova, Snezhana. Stability of Caputo fractional differential equations by Lyapunov functions. Applications of Mathematics, Tome 60 (2015) no. 6, pp. 653-676. doi: 10.1007/s10492-015-0116-4

Cité par Sources :