Fractional Reaction-Diffusion

By B. Henry, S. Wearne. 2000

318 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/75b2d138e3d1a94bf3f8058495d4cb4e4b1015c5

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In Condensed Matter Physics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

A finite element method for time fractional partial differential equations (2011, unknown): “[3], [4], [14], [15], [24], [25], [28], [29].”
A Convergent Algorithm for Solving Higher-Order Nonlinear Fractional Boundary Value Problems (2015, unknown): “see, by way of example not exhaustive enumeration, [1], [2], [7], [9], [12], [13], [16], [20], [21], [22], [24], [28], [31], [32], [41], [43], [37], [44] and the many references therein.”
A Space-Time Spectral Method for the Time Fractional Diffusion Equation (2009, background): “Related equations of importance are the space/time fractional diffusion equations, the fractional advection-diffusion equation [11, 12] for anomalous diffusion with sources and sinks, and the fractional Fokker-Planck equation [3] for anomalous diffusion in an external field, etc.”
Discrete random walk models for space-time fractional diffusion (2002, unknown): “[1], [10], [15], [28] [29, 30], [34, 35, 36], [40], [48, 49], [52], [57], [61, 62], [63, 64].”
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, background): “Compare the derivation in Henry and Wearne (2000).”
Numerical solution via Laplace transforms of a fractional order evolution equation (2010, methodology): “The methods are combined with finite element discretization in the spatial variables to yield fully discrete methods.”
Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation (2010, background): “Related equations of importance are the space/time fractional diffusion equations, the fractional advection-diffusion equation [17, 18] for anomalous diffusion with sources and sinks, and the fractional FokkerPlanck equation [4] for anomalous diffusion in an external field, etc.”
A fractional‐order Jacobi Tau method for a class of time‐fractional PDEs with variable coefficients (2016, background): “A striking example of this is a model for anomalous transport processes and diffusion, leading to fractional PDEs [1], but other examples are readily available for generalizing many classical problems in mathematical physics, including the fractional Burgers’ equation [2, 3], the fractional Fokker–P”
Regularity of solutions to a time-fractional diffusion equation (2010, background): “We can interpret the parameter ν at the microscopic level [6, 12]: the diffusing particles have a mean-square displacement 2Kt/Γ(1 + ν) ∝ t.”
Mathematical modeling of time fractional reaction-diffusion systems (2008, unknown): “to these systems, which is a fractional derivative index, and it gives a great degree of freedom for diversity of selforganization phenomena and new nonlinear effects [10,11,27,32,15] depending on the order of time-space fractional derivatives.”