  In quantum mechanics, the space-fractional Schr\"{o}dinger equation provides
a natural extension of the standard Schr\"{o}dinger equation when the Brownian
trajectories in Feynman path integrals are replaced by Levy flights. Here an
optical realization of the fractional Schr\"{o}dinger equation, based on
transverse light dynamics in aspherical optical cavities, is proposed. As an
example a laser implementation of the fractional quantum harmonic oscillator is
presented, in which dual Airy beams can be selectively generated under off-axis
longitudinal pumping.
