  We present a physical example, where a fractional (both in space and time)
Schr\"odinger equation appears only as a formal effective description of
diffusive wave transport in complex inhomogeneous media. This description is a
result of the parabolic equation approximation that corresponds to the paraxial
small angle approximation of the fractional Helmholtz equation. The obtained
effective quantum dynamics is fractional in both space and time. As an example,
L\'evy flights in an infinite potential well are considered numerically. An
analytical expression for the effective wave function of the quantum dynamics
is obtained as well.
