  In this paper, we introduced the local and global mixed Morrey-type spaces,
and some properties of these spaces are also studied. After that, the necessary
conditions of the boundedness of fractional integral operators $I_{\alpha}$ are
studied respectively in mixed-norm Lebesgue spaces and the local mixed
Morrey-type spaces. Last but not least, the boundedness of $I_{\alpha}$ is
obtained by Hardy operators' boundedness in weighted Lebesgue spaces. As
corollaries, we acquire the boundedness of $I_{\alpha}$ in mixed Morrey
spaces(\hyperlink{Corollary 5.6}{Corollary 5.6}) and mixed Lebesgue
spaces(\hyperlink{Corollary 5.7}{Corollary 5.7}) respectively. Particularly,
\hyperlink{Corollary 5.7}{Corollary 5.7} obtains a sufficient and necessary
condition.
