  We investigate the propagation of one-dimensional and two-dimensional (1D,
2D) Gaussian beams in the fractional Schr\"odinger equation (FSE) without a
potential, analytically and numerically. Without chirp, a 1D Gaussian beam
splits into two nondiffracting Gaussian beams during propagation, while a 2D
Gaussian beam undergoes conical diffraction. When a Gaussian beam carries
linear chirp, the 1D beam deflects along the trajectories $z=\pm2(x-x_0)$,
which are independent of the chirp. In the case of 2D Gaussian beam, the
propagation is also deflected, but the trajectories align along the diffraction
cone $z=2\sqrt{x^2+y^2}$ and the direction is determined by the chirp. Both 1D
and 2D Gaussian beams are diffractionless and display uniform propagation. The
nondiffracting property discovered in this model applies to other beams as
well. Based on the nondiffracting and splitting properties, we introduce the
Talbot effect of diffractionless beams in FSE.
