The fractional‐order governing equation of Lévy Motion

By David A. Benson, S. Wheatcraft, Mark M. Meerschaert. 2000

774 citations recorded by the source corpus.

Subfields: Computational Mechanics, Modeling and Simulation, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/61ddfb882971908dea79f7e2ce003a5fd7b02232

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In Computational Mechanics

In Modeling and Simulation

In Ocean Engineering

Citations in the corpus

Possible problems of scale dependency in applications of the three‐dimensional fractional advection‐dispersion equation to natural porous media (2002, methodology): “…explanation for the observed scale dependence of the traditional dispersivity is that the resulting dispersion is based on the mechanics of Brownian motion [Benson et al., 2000, 2001], while macroscopic random trajectories in heterogeneous porous media may be better described by Levy motion.”
Parameter estimation for fractional transport: A particle‐tracking approach (2009, background): “Parameter estimation for fractional transport:”
A Fourier method for the fractional diffusion equation describing sub-diffusion (2007, methodology): “[8],[9] used a fractional advection-dispersion equation to simulate transport processes with heavy tails and demonstrated the equivalence between these heavy-tailed motions and transport equations that use fractional-order derivatives.”
Diffusion in Porous Media: Phenomena and Mechanisms (2019, methodology): “CTRW is related to both Levy walk models (Metzler and Klafter 2000; Cushman et al. 2009) and fractional advection–dispersion equations (Benson et al. 2000; Cushman and Ginn 2000) that are characterized by spatiotemporal kernel functions with an asymptotic powerlaw scaling.”
Modeling non‐Fickian transport in geological formations as a continuous time random walk (2006, background): “[225] In contrast to the temporal FDE a spatial FDE assumes a transition time distribution y(t) with a finite first moment and a transition length distribution p(s) with a diverging second moment.”
Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, methodology): “This similarity might be the motivation behind the application of the space nonlocal model to simulate the retention process (see for example, [12,45,46,74,143]).”