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Fractional averaging theory for discrete fractional-order system with impulses
Peiguang Wang1, Xiang Liu2, Douglas R Anderson3
1School of Mathematics and Information Science, Hebei University, Baoding 071002, China.
Abstract:
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.
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