  The article produces a brief review of some recent results which predict
stable propagation of solitons and solitary vortices in models based on the
nonlinear Schroedinger equation including fractional one- or two-dimensional
diffraction and cubic or cubic-quintic nonlinear terms, as well as linear
potentials. The fractional diffraction is represented by fractional-order
spatial derivatives of the Riesz type, defined in terms of the direct and
inverse Fourier transform. In this form, it can be realized by spatial-domain
light propagation in optical setups with a specially devised combination of
mirrors, lenses, and phase masks. The results presented in the article were
chiefly obtained in a numerical form. Some analytical findings are included too
-- in particular, for fast moving solitons, and results produced by the
variational approximation. Also briefly considered are dissipative solitons
which are governed by the fractional complex Ginzburg-Landau equation.
