In this brief, we contribute to adaptive neural network (NN) backstepping control design for the nonlinear double-integrator fractional-order (FO) systems comprising unknown dynamics and disturbances by the event-triggered procedure. To this end, a new triggering rule with a dynamical variable is first introduced, including some available static triggering rules as its particular form. Then, by using the contradiction and some properties of the Mittag-Leffler function, it is proved for the first time that the applied dynamical variable is positive and bounded for the FO systems. Hence, the inter-event time between any two successive triggering moments can be enlarged than static event-triggered results. By integrating the backstepping approach into the NN, an adaptive NN controller is constructed, which introduces a new analysis viewpoint on the Zeno phenomenon avoidance for the FO controllers. Under this controller, the tracking error converges to a small compact set including the origin. Finally, an example is given to show the feasibility of the proposed method.

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