  We analyze the propagation dynamics of radially polarized symmetric Airy
beams (R-SABs) in a (2+1)-dimensional optical system with fractional
diffraction, modeled by the fractional Schr\"odinger equation (FSE)
characterized by the L\'evy index. The autofocusing effect featured by such
beams becomes stronger, while the focal length becomes shorter, with the
increase of . The effect of the intrinsic vorticity on the autofocusing
dynamics of the beams is considered too. Then, the ability of R-SABs to capture
nano-particles by means of radiation forces is explored, and multiple capture
positions emerging in the course of the propagation are identified. Finally, we
find that the propagation of the vortical R-SABs with an off-axis shift leads
to rupture of the ring-shaped pattern of the power-density distribution.
