Commutative Caputo Fractional Korovkin Approximation for Stochastic Processes

Here we consider and study expectation commutative stochastic positive linear operators acting on L1-continuous stochastic processes which are Caputo fractional differentiable. Under some mild, general and natural assumptions on the stochastic processes we produce related Caputo fractional stochastic Shisha-Mond type inequalities pointwise and uniform. All convergences are produced with rates and are given by the fractional stochastic inequalities involving the first modulus of continuity of the expectation of the αth right and left fractional derivatives of the engaged stochastic process, (Formula Presented). The amazing fact here is that the basic real Korovkin test functions assumptions impose the conclusions of our Caputo fractional stochastic Korovkin theory. We include also a detailed application to stochastic Bernstein operators. See also[11]