  We introduce a system of propagation equations for the fundamental-frequency
(FF) and second-harmonic (SH) waves in the bulk waveguide with the effective
fractional diffraction and quadratic (chi ^(2)) nonlinearity. The numerical
solution produces families of ground-state (zero-vorticity) two-dimensional
solitons in the free space, which are stable in exact agreement with the
Vakhitov-Kolokolov criterion, while vortex solitons are completely unstable in
that case. Mobility of the stable solitons and inelastic collisions between
them are briefly considered too. In the presence of a harmonic-oscillator (HO)
trapping potential, families of partially stable single- and two-color solitons
(SH-only or FF-SH ones, respectively) are obtained, with zero and nonzero
vorticities. The single-and two-color solitons are linked by a bifurcation
which takes place withthe increase of the soliton's power.
