Stochastic model for ultraslow diffusion

By Mark M. Meerschaert, Hans-Peter Scheffler. 2006

132 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9e28c08ba96457634365f8f2f4c32cf79f4f997a

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In Applied Mathematics

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Distributed order calculus and equations of ultraslow diffusion (2007, background): “The solutions in [22] are understood as solutions of “algebraic” equations obtained if the Laplace transform in t and the Fourier transform in x are applied.”
Time fractional equations and probabilistic representation (2017, background): “The time fractional derivative ∂ w t defined in this paper is the distributed-order fractional derivative defined in [18].”
Triangular array limits for continuous time random walks (2008, methodology): “5 in [40] shows that under certain regular variation assumptions on the mixing density p(β) we have {T (ct)}t≥0 ⇒ {D(t)}t≥0 as c → ∞”
On fractional Duhamel's principle and its applications (2010, background): “For more information about recent results on the Cauchy problem for abstract fractional differential-operator equations, we refer the reader to [3, 10, 16]; and for a recent mathematical treatment of the distributed fractional order differential equations to papers [18, 23, 35].”
BOUNDARY VALUE PROBLEMS FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATION OF DISTRIBUTED ORDER (2009, unknown): “in [11], [17], and [24].”
Numerical Computation of First-Passage Times of Increasing Lévy Processes (2009, methodology): “It follows from Remark 5.3 in Meerschaert and Scheffler (2006 ) t hatM has one-time marginal densities which solve Eq. 43. This fact is useful because it allows us to study the solutions of Eq. 43 using properties of M. For example, a common way to measure how quick particles “spread out” under the”
Space-time fractional diffusion on bounded domains (2011, background): “Distributed-order time-fractional diffusion equations can be used to model ultraslow diffusion, in which a cloud of particles spreads at a logarithmic rate, also called Sinai diffusion [23].”
General Fractional Calculus, Evolution Equations, and Renewal Processes (2011, background): “where ρ is a Borel measure on [0, 1]; see [1, 6, 11, 14, 15, 16, 17, 21, 28].”
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations (2014, unknown): “However, in [16] a CTRW model was suggested with the property that the scaling limits of these random walks are subordinated random processes whose density functions solve a distributed order fractional diffusion equation.”
Distributed-order fractional diffusions on bounded domains (2009, background): “20) in [26], we have 1 s ψW (s)e −ψW (s)l = ∞ ∫”