  We have investigated the propagation dynamics of the circular Airy Gaussian
vortex beams (CAGVBs) in a (2+1)-dimesional optical system discribed by
fractional nonlinear Schr\"odinger equation (FNSE). By combining fractional
diffraction with nonlinear effects, the abruptly autofocusing effect becomes
weaker, the radius of the focusing beams becomes bigger and the autofocusing
length will be shorter with increase of fractional diffraction L\'evy index. It
has been found that the abruptly autofocusing effect becomes weaker and the
abruptly autofocusing length becomes longer if distribution factor of CAGVBs
increases for fixing the L\'evy index. The roles of the input power and the
topological charge in determining the autofocusing properties are also
discussed. Then, we have found the CAGVBs with outward acceleration and shown
the autodefocusing properties. Finally, the off-axis CAGVBs with positive
vortex pairs in the FNSE optical system have shown interesting features during
propagation.
