  We report solutions for solitons of the "accessible" type in globally
nonlocal nonlinear media of fractional dimension (FD), viz., for self-trapped
modes in the space of effective dimension $2<D\le3$ with harmonic-oscillator
potential whose strength is proportional to the total power of the wave field.
The solutions are categorized by a combination of radial, orbital and azimuthal
quantum numbers $(n,l,m)$. They feature coaxial sets of vortical and
necklace-shaped rings of different orders, and can be exactly written in terms
of special functions that include Gegenbauer polynomials, associated Laguerre
polynomials, and associated Legendre functions. The validity of these solutions
is verified by direct simulation. The model can be realized in various physical
settings emulated by FD spaces; in particular, it applies to excitons trapped
in quantum wells.
