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Keldysh Institute preprints, 2014, 018, 21 pp. (Mi ipmp1870)  

This article is cited in 1 scientific paper (total in 1 paper)

On the application of Riemann–Liouville fractional calculus to the analysis of probability distributions

D. A. Zenyuk, Yu. N. Orlov


Abstract: In this paper some issues of application of Riemann–Liouville operators to the analysis of absolutely continuous distributions are considered. In general case such transition considerably change common properties of probability densities, making standard statistical techniques infeasible. It is shown that Fokker–Planck equation may have multiple analogues of fractional order. It is also demonstrated that fractional equations of Fokker–Planck type do not permit ordinary hydrodynamical substitution.

Keywords: fractional calculus, Riemann–Liouville operators, probability measure, distribution functions.

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UDC: 519.213

Citation: D. A. Zenyuk, Yu. N. Orlov, “On the application of Riemann–Liouville fractional calculus to the analysis of probability distributions”, Keldysh Institute preprints, 2014, 018, 21 pp.

Citation in format AMSBIB
\Bibitem{ZenOrl14}
\by D.~A.~Zenyuk, Yu.~N.~Orlov
\paper On the application of Riemann--Liouville fractional calculus to the analysis of probability distributions
\jour Keldysh Institute preprints
\yr 2014
\papernumber 018
\totalpages 21
\mathnet{http://mi.mathnet.ru/ipmp1870}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Zenyuk, L. V. Klochkova, Yu. N. Orlov, “Modelirovanie nestatsionarnykh sluchainykh protsessov kineticheskimi uravneniyami s drobnymi proizvodnymi”, Zhurnal SVMO, 18:2 (2016), 125–133  mathnet  elib
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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