  This paper addresses issues surrounding the concept of fractional quantum
mechanics, related to lights propagation in inhomogeneous nonlinear media,
specifically restricted to a so called gravitational optics. Besides
Schr\"odinger Newton equation, we have also concerned with linear and nonlinear
Airy beam accelerations in flat and curved spaces and fractal photonics,
related to nonlinear Schr\"odinger equation, where impact of the fractional
Laplacian is discussed. Another important feature of the gravitational optics'
implementation is its geometry with the paraxial approximation, when quantum
mechanics, in particular, fractional quantum mechanics, is an effective
description of optical effects. In this case, fractional-time differentiation
reflexes this geometry effect as well.
