Geodesic
A probabilistic approximation of the Cauchy problem solution for the Schr\"odinger equation with a~fractional derivative operator
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 257-272

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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. 
@article{ZNSL_2017_466_a16,
     author = {M. V. Platonova and S. V. Tsykin},
     title = {A probabilistic approximation of the {Cauchy} problem solution for the {Schr\"odinger} equation with a~fractional derivative operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {257--272},
     publisher = {mathdoc},
     volume = {466},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a16/}
}
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M. V. Platonova; S. V. Tsykin. A probabilistic approximation of the Cauchy problem solution for the Schr\"odinger equation with a~fractional derivative operator. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 257-272. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a16/