Stability of caputo fractional differential equations with non-instantaneous impulses

The stability of the zero solution of a nonlinear Caputo fractional differential equa- tion with noninstantaneous impulses is studied using Lyapunov like functions. The theory is based on the derivative of a Lyapunov like function along the given noninstantaneous impulsive fractional differential equations. Two types of fractional derivatives of Lyapunov functions are introduced and their applications are discussed. Several suffcient conditions for uniform stability and asymptotic uniform stability of the zero solution, based on the definition of the derivative of Lyapunov functions are established. Some examples are given to illustrate the results.