Noninstantaneous impulses in Caputo fractional differential equations and practical stability via Lyapunov functions

Practical stability of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. We present a new definition of the derivative of a Lyapunov like function along the given fractional differential equation with noninstantaneous impulses. Sufficient conditions for practical stability, practical quasi stability and strongly practical stability are established and several examples are given to illustrate the results.