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We show that the fractional integral operator 
$I_{\alpha }$, 
$0<\alpha <n$, and the fractional maximal operator 
$M_{\alpha }$, 
$0\le \alpha <n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet–Morrey spaces. The results for the fractional maximal operator 
$M_\alpha $ are extensions of the work of Tang [‘Choquet integrals, weighted Hausdorff content and maximal operators’, Georgian Math. J. 18(3) (2011), 587–596] and earlier work of Adams and Orobitg and Verdera. The results for the fractional integral operator 
$I_{\alpha }$ are essentially new.
