Here, we research the expectation commutative stochastic positive linear operators acting on $L^{1}$-continuous stochastic processes which are conformable fractional differentiable. Under some mild, general and natural assumptions on the stochastic processes we produce related conformable fractional stochastic Shisha-Mond type inequalities pointwise and uniform. All convergences are produced quantitatively and are given by the conformable fractional stochastic inequalities involving the first modulus of continuity of he expectation of the $\alpha $-th right and left conformable fractional derivatives of the engaged stochastic process, $\alpha \in ( n,n+1) $, $n\in \mathbb{Z}_{+}$. The amazing fact here is that the simple real Korovkin test functions assumptions imply the conclusions of our conformable fractional stochastic Korovkin theory. Weinclude also a full details application to stochastic Bernstein operators.