  We demonstrate that beams originating from Fresnel diffraction patterns are
self-accelerating in free space. In addition to accelerating and self-healing,
they also exhibit parabolic deceleration property, which is in stark contrast
to other accelerating beams. We find that the trajectory of Fresnel paraxial
accelerating beams is similar to that of nonparaxial Weber beams. Decelerating
and accelerating regions are separated by a critical propagation distance, at
which no acceleration is present. During deceleration, the Fresnel diffraction
beams undergo self-smoothing, in which oscillations of the diffracted waves
gradually focus and smooth out at the critical distance.
