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- W2134264301 abstract "Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus." @default.
- W2134264301 created "2016-06-24" @default.
- W2134264301 creator A5017384955 @default.
- W2134264301 creator A5065690438 @default.
- W2134264301 creator A5086748121 @default.
- W2134264301 date "2013-01-01" @default.
- W2134264301 modified "2023-10-03" @default.
- W2134264301 title "Fractional calculus in hydrologic modeling: A numerical perspective" @default.
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- W2134264301 cites W1494534457 @default.
- W2134264301 cites W1653492212 @default.
- W2134264301 cites W1659987100 @default.
- W2134264301 cites W1673649620 @default.
- W2134264301 cites W1824925390 @default.
- W2134264301 cites W1941092083 @default.
- W2134264301 cites W1956551449 @default.
- W2134264301 cites W1965761202 @default.
- W2134264301 cites W1969965325 @default.
- W2134264301 cites W1975172081 @default.
- W2134264301 cites W1977360274 @default.
- W2134264301 cites W1987900357 @default.
- W2134264301 cites W1989941945 @default.
- W2134264301 cites W1991400784 @default.
- W2134264301 cites W1998837235 @default.
- W2134264301 cites W2000123139 @default.
- W2134264301 cites W2000659785 @default.
- W2134264301 cites W2000871758 @default.
- W2134264301 cites W2002585486 @default.
- W2134264301 cites W2006683380 @default.
- W2134264301 cites W2008387167 @default.
- W2134264301 cites W2008771294 @default.
- W2134264301 cites W2017940889 @default.
- W2134264301 cites W2020763891 @default.
- W2134264301 cites W2025672056 @default.
- W2134264301 cites W2029120512 @default.
- W2134264301 cites W2030026750 @default.
- W2134264301 cites W2030865888 @default.
- W2134264301 cites W2031706088 @default.
- W2134264301 cites W2037973974 @default.
- W2134264301 cites W2038874864 @default.
- W2134264301 cites W2044412303 @default.
- W2134264301 cites W2046579020 @default.
- W2134264301 cites W2048225788 @default.
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- W2134264301 cites W2075093641 @default.
- W2134264301 cites W2081945469 @default.
- W2134264301 cites W2088216803 @default.
- W2134264301 cites W2088847873 @default.
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- W2134264301 cites W2094568796 @default.
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- W2134264301 cites W2096890836 @default.
- W2134264301 cites W2096931175 @default.
- W2134264301 cites W2098426070 @default.
- W2134264301 cites W2099111135 @default.
- W2134264301 cites W2102541369 @default.
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- W2134264301 cites W2109582427 @default.
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- W2134264301 cites W2142758723 @default.
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- W2134264301 cites W2161378850 @default.
- W2134264301 cites W4241317018 @default.
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- W2134264301 cites W4250501155 @default.
- W2134264301 doi "https://doi.org/10.1016/j.advwatres.2012.04.005" @default.
- W2134264301 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/3603590" @default.
- W2134264301 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/23524449" @default.
- W2134264301 hasPublicationYear "2013" @default.
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