  In this paper, the authors define the mixed $\lambda$-central Morrey spaces
and the mixed $\lambda$-central $BMO$ spaces. The boundedness of the fractional
integral operators $T_{\alpha}$ and its commutators $[b, T_{\alpha}]$ are
established on the mixed $\lambda$-central Morrey spaces, respectively.
Furthermore, we also extend these results to the generalized mixed central
Morrey spaces.
