On a limit theorem related to a Cauchy problem solution for the Schrödinger equation with a fractional derivative operator of the order $\alpha\in\bigcup\limits_{m=3}^{\infty}(m-1, m)$

We prove a limit theorem on convergence of mathematical expectations of functionals of sums of independent random variables to a Cauchy problem solution for the nonstationary Schrödinger equation with a symmetric fractional derivative operator of the order $\alpha\in\bigcup\limits_{m=3}^{\infty}(m-1, m)$ in the right hand side.