  The generalized mean-square fractional integrals
$\mathcal{J}_{\rho,\lambda,u+;\omega}^{\sigma}$ and
$\mathcal{J}_{\rho,\lambda,v-;\omega}^{\sigma}$ of the stochastic process $X$
are introduced. Then, for Jensen-convex and strongly convex stochastic
proceses, the generalized fractional Hermite--Hadamard inequality is establish
via generalized stochastic fractional integrals.
