Fractional vector calculus for fractional advection–dispersion

By Mark M. Meerschaert, J. Mortensen, S. Wheatcraft. 2006

190 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d4058afe73e13959d0b9f62934b100642da388ad

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In Biomedical Engineering

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

A Fractional Model of Continuum Mechanics (2012, methodology): “For materials for which (4.14) is satisfied and a specific choice of region H , we introduce the fractional order gradient which is a generalized form of the fractional gradient introduced in [ 37 ]:”
Fractional Calculus as a Mathematical Tool to Improve the Modeling of Mass Transfer Phenomena in Food Processing (2012, background): “When the so-called tails of the concentration profile show a slow decay, this is a clear feature of fractional phenomena [37].”
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, background): “The paper [38] introduces a fractional divergence enabling the consideration of a fractional flux.”
Fractional Vector Calculus and Fractional Maxwell's Equations (2008, methodology): “egral operations (ﬂux, circulation), and the theorems of Gauss, Stokes and Green. 2.3 Meerschaert-Mortensen-Wheatcraft fractional vector calculus In the paper of Meerschaert, Mortensen and Wheatcraft [21], a fractional generalization of curl operator has been suggested as curlαF = e lεlmnDmI 1−α n F”
What is the fractional Laplacian? A comparative review with new results (2018, unknown): “Here, Dθ (·) is the Riemann-Liouville fractional directional derivative [51] given by Dθ (·) = (θ · ∇)I1−α θ (·) for 0 < α < 1; Dθ (·) = (θ · ∇)2 I2−α θ (·) for 1 < α < 2; where θ · ∇ =∑di=1 θi ∂ ∂xi is the directional derivative, thus (θ · ∇)2 =∑dj=1∑di=1 θiθ j ∂2 ∂x j∂xi , and the fractional direc”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, background): “(5) Applications of fractional vector calculus in mathematical physics and probability, in particular in fluid mechanics [64, 87].”
Fractional advection‐dispersion equations for modeling transport at the Earth surface (2009, methodology): “[28] An alternative Eulerian derivation of the space fADE uses a fractional conservation of mass with a traditional Fickian flux [Meerschaert et al., 2006].”
Parameter estimation for fractional transport: A particle‐tracking approach (2009, background): “Recent work by Meerschaert et al. [2006] outlines a more general approach that includes a fractional divergence (fractional conservation of mass).”
Fractional calculus: A survey of useful formulas (2013, unknown): “[21–24] and the references therein.”
Fractional conservation of mass (2008, methodology): “[11].”
On a new class of fractional partial differential equations (2014, background): “Indeed, the literature on fractional derivatives in one dimension is quite extensive4, while in several dimensions there have been other possible de nitions due to Meerschaert, Mortensen and Wheatcraft [22] or Tarasov [32].”
A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, methodology): “Bueno-Orovio, Kay, and Burrage [3] proposed a fundamental rethinking of the homogenization approach via the use of a fractional Fick’s law (see [24, 27]) and, in particular, we introduce a fractional FitzHugh– Nagumo monodomain model in which we capture the spatial heterogeneities and spatial connec”