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We introduce axisymmetric Airy-Gaussian vortex beams in a model of an opticalsystem based on the (2+1)-dimensional fractional Schr\"odinger equation,characterized by its L\'evy index (LI). By means of numerical methods, weexplore propagation dynamics of the beams with vorticities from 0 to 4. Thepropagation leads to abrupt autofocusing, followed by its reversal (reboundfrom the center). It is shown that LI, the relative width of the Airy andGaussian factors, and the vorticity determine properties of the autofocusingdynamics, including the focusing distance, radius of the focal light spot, andpeak intensity at the focus. A maximum of the peak intensity is attained atintermediate values of LI, close to LI=1.4 . Dynamics of the abruptautofocusing of Airy-Gaussian beams carrying vortex pairs (split doublevortices) is considered too.

Propagation dynamics of abruptly autofocusing circular Airy-Gaussian vortex beams in the fractional Schr\"odinger equation