In this paper the statement of initial value problems for fractional
differential equations with noninstantaneous impulses is given. These
equations are adequate models for phenomena that are characterized by
impulsive actions starting at arbitrary fixed points and remaining active on
finite time intervals. Strict stability properties of fractional differential
equations with non-instantaneous impulses by the Lyapunov approach is
studied. An appropriate definition (based on the Caputo fractional Dini
derivative of a function) for the derivative of Lyapunov functions among the
Caputo fractional differential equations with non-instantaneous impulses is
presented. Comparison results using this definition and scalar fractional
differential equations with non-instantaneous impulses are presented and
sufficient conditions for strict stability and uniform strict stability are
given. Examples are given to illustrate the theory.
Uniformly Regular Triangulations for Parameterizing Lyapunov Functions
