Based on the generalized Huygens-Fresnel principle and the non-Kolmogorov spectral model, the expressions for the Rayleigh range zR and the turbulence distance zT of radial partially coherent Gaussian-Schell model array beams of the free space optics system propagating through non- Kolmogorov turbulence were derived. And the expressions were used to analyze numerically the changes of the Rayleigh range and the turbulence distance with turbulence parameters and beams parameters. The results show that for both coherent and incoherent combinations, the dependence of zR and zT of the radial partially coherent Gaussian-Schell model array beams on generalized parameter α is not monotonic. When α=3.11, zR and zT reach their minima, and this means that the beams spreading is largest. For the coherent combination of beams spreading is smaller than that for the coherent combination, but it is larger affected by turbulence; For coherent combinations, the larger the radial distribution radius r0, the larger the Rayleigh range zR and turbulence distance zT of the combined beam, but incoherent combinations is not affected; for both coherent and incoherent combinations, the number of sub-beams has no influence on the Rayleigh range and the turbulent distance of the combined beam; When beams coherent parameter β is small enough and wavelength λ is large enough, the influence of turbulence on zR can be ignored.