  In this paper, we first introduce some new Morrey type spaces containing
generalized Morrey space and weighted Morrey space with two weights as special
cases. Then we give the weighted strong type and weak type estimates for
fractional integral operators $I_\alpha$ in these new Morrey type spaces.
Furthermore, the weighted strong type estimate and endpoint estimate of linear
commutators $[b,I_{\alpha}]$ formed by $b$ and $I_{\alpha}$ are established.
Also we study related problems about two-weight, weak type inequalities for
$I_{\alpha}$ and $[b,I_{\alpha}]$ in the Morrey type spaces and give partial
results.
