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

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