A probabilistic approximation of the Cauchy problem solution for the Schrödinger equation with a fractional derivative operator

We construct two types of probabilistic approximations of the Cauchy problem solution for the nonstationary Schrödinger equation with a symmetric fractional derivative of order $\alpha\in(1,2)$ on the right hand side. In the first case we approximate the solution by a mathematical expectation of point Poisson field functionals and in the second case we approximate the solution by a mathematical expectation of functionals of sums of independent random variables with a power asymptotics of a tail distribution.