<p>Optical vortices with arbitrary topological charges can be theoretically generated at the same output plane when fractionally Fourier-transformed Gaussian Schell-model vortex beams propagate in free space. The derived theoretical formula indicates that the position of generated optical vortices with arbitrary topological charges remains independent of topological charges, conversely, it depends on both the Rayleigh range and the angle of fractional Fourier transforms. Furthermore, the field depth of optical vortices is scarcely influenced by varying topological charges. In contrast, it is affected by both the coherence length and the angle of fractional Fourier transforms. Our results have potential applications in free-space optical communication, and also provide new ideas and methods for future optical design and applications.</p>