  We demonstrate that, with the help of a Gaussian potential barrier, dark
modes in the form of a local depression ("bubbles") can be supported by the
repulsive Kerr nonlinearity in combination with fractional dimension.
Similarly, W-shaped modes are supported by a double potential barrier. Families
of the modes are constructed in a numerical form, and also by means of the
Thomas-Fermi and variational approximations. All these modes are stable, which
is predicted by computation of eigenvalues for small perturbations and
confirmed by direct numerical simulations.
