Fractional averaging theory for discrete fractional-order system with impulses.

In this paper, we improve the averaging theory on both finite and infinite time intervals for discrete fractional-order systems with impulses. By employing new techniques, generalized impulsive discrete fractional-order Gronwall inequality is introduced. In addition, the closeness of solutions for the discrete fractional-order systems with impulses and the averaged discrete fractional-order systems with impulses is derived. Finally, three examples are provided to illustrate the efficiency of our main results.