Based on the fractional Schrdinger equation with variable coefficients, the influence of chirp on the propagation characteristics of Airy beams is studied analytically and numerically. When the initial Airy beam has no chirp, it splits into two Airy-like wave packets with equal intensity. For the action of the longitudinal periodic modulation, the beam presents a periodic focusing behavior. When the initial Airy beam has a quadratic chirp, it causes the Airy beam to split into two wave packets with unequal intensities. Under the action of the longitudinal periodic modulation, it exhibits periodic oscillation behavior, and the Airy beam is restored at the focus point of the two beams. Then the influence of related parameters on the dynamics of the second chirped Airy beam is analyzed. The results show that the existence of a chirp has an inhibitory effect on the split beam, and the larger the value of the chirp, the more obvious the inhibitory effect on the split beam. Different signs of the chirp have different effects on the transmission of the light beam. The positive chirp inhibits the right split, and the negative chirp inhibits the left split. It is because of this suppression that interference fringes become less and less obvious. When the chirp parameter is constant, as the Lévy index increases until α=2, Airy beam appears to be inverted. In addition, the influence of related parameters on the interaction of the double Airy beams is also considered. We find that the focal positions of the two beams change with the distance between the two Airy beams, and the number of focal points of the two beams increases with the increase of the Lévy index. The results show that the Airy beams can be controlled by adjusting the parameters to realize the beam management in the fractional Schrdinger equation.