Abstract: Using the two-component Ginzburg-Landau model, we investigate the effect of sample size and magnitude and homogeneity of external magnetic field on the stability of fractional vortex states in a mesoscopic two-band superconducting disk. We found that each fractional state has a preferable sample size, for which the range of applied field in which the state is stable is pronouncedly large. Vice versa, there exists an optimal magnitude of applied field for which a large range of possible sample radii will support the considered fractional state. Finally, we show that the stability of fractional states can be enhanced even further by magnetic nanostructuring of the sample, i.e. by suitably chosen geometrical parameters and magnetic moment of a ferromagnetic dot placed on top of the superconducting disk. (C) 2014 Elsevier B.V. All rights reserved.