Stability of Caputo fractional differential equations by Lyapunov functions

[摘要] 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.

[学科分类] 应用数学

[关键词] stability;Caputo derivative;Lyapunov function;fractional differential equation