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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 474, Pages 199–212 (Mi znsl6679)  

This article is cited in 2 scientific papers (total in 2 papers)

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

M. V. Platonovaabc, S. V. Tsykincab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Saint Petersburg State University, Saint Petersburg, Russia
c Saint Petersburg State University, Saint Petersburg, Russia
Full-text PDF (188 kB) Citations (2)
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Abstract: We construct a probabilistic approximation of the Cauchy problem solution for the nonstationary Schrödinger equation with a symmetric fractional derivative of order $\alpha\in\bigcup\limits_{m=3}^{\infty}(m-1, m)$ in the right hand side.
Key words and phrases: fractional derivative, Schrödinger equation, limit theorem, point Poisson field.
Funding agency Grant number
Russian Science Foundation 14-21-00035
Russian Foundation for Basic Research 16-01-00443_а
Received: 29.10.2018
Document Type: Article
UDC: 519.2
Language: Russian
Citation: M. V. Platonova, S. V. Tsykin, “Probabilistic approach to Cauchy problem solution for the Schrödinger equation with a fractional derivative of order $\alpha\in\bigcup\limits_{m=3}^{\infty}(m-1, m)$”, Probability and statistics. Part 27, Zap. Nauchn. Sem. POMI, 474, POMI, St. Petersburg, 2018, 199–212
Citation in format AMSBIB
\Bibitem{PlaTsy18}
\by M.~V.~Platonova, S.~V.~Tsykin
\paper Probabilistic approach to Cauchy problem solution for the Schr\"odinger equation with a fractional derivative of order $\alpha\in\bigcup\limits_{m=3}^{\infty}(m-1, m)$
\inbook Probability and statistics. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 474
\pages 199--212
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6679}
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  • https://www.mathnet.ru/eng/znsl/v474/p199
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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