Mittag-Leffler Stability of Impulsive Nonlinear Fractional-Order Systems with Time Delays.

Stability analysis of impulsive nonlinear fractional-order system (FOS) is discussed. First, the existence and uniqueness of solutions for FOS is discussed with help of fixed point theory. The nonlinear system is considered with a constant time delay and impulsive effects. Then, novel sufficient conditions to prove the Mittag-Leffler stability (MLS) of FOS are established by using well known mathematical techniques. Also, the results are extended to present finite-time MLS conditions for considered nonlinear FOSs. Finally, examples are given to show the validity of the derived results.