  We investigate the stability of noncomposite fractional vortex states in a
mesoscopic two-band superconductor within the two-component Ginzburg-Landau
model. Our analysis explicitly takes into account the relationship between the
model parameters and microscopic material parameters, such as partial density
of states, fermi velocities and elements of the electron-phonon coupling
matrix. We have found that states with different phase winding number in each
band (L1 not equal to L2) and fractional flux can exist in many different
configurations, including rather unconventional ones where the dominating band
carries larger winding number and states where |L1-L2| > 1. We present a
detailed analysis of the stability of the observed vortex structures with
respect to changing the microscopic parameters, showing that, in the weak
coupling case, fractional vortex states can be assessed in essentially the
whole range of temperatures and applied magnetic fields in which both bands are
active. Finally, we propose an efficient way of increasing the range of
parameters for which these fractional vortex states can be stabilized. In
particular, our proposal allows for observation of fractional vortex structures
in materials with stronger coupling, where those states are forbidden at a
homogeneous field. This is accomplished with the help of the stray fields of a
suitably prepared magnetic dot placed nearby the superconducting disk.
