  We introduce a model which gives rise to self-trapping of fundamental and
higher-order localized states in a one-dimensional nonlinear Schr\"odinger
equation with fractional diffraction and the strength of the self-defocusing
nonlinearity growing steeply enough from the center to periphery. The model can
be implemented in a planar optical waveguide. Stability regions are identified
for the fundamental and dipole (single-node) states in the plane of the L\'evy
index and the total power (norm), while states of higher orders are unstable.
Evolution of unstable states is investigated too, leading to spontaneous
conversion towards stable modes with fewer node.
