Distributed-Order Fractional Kinetics

By Igor M. Sokolov, Aleksei V. Chechkin, Joseph Klafter. 2004

247 citations recorded by the source corpus.

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by distributed-order equations. In the present paper we consider different forms of distributed-order fractional kinetic equations and investigate the effects described by different classes of such equations. In particular, the equations describing accelerating and decelerating subdiffusion, as well as the those describing accelerating and decelerating superdiffusion are presented.

Subfields: Modeling and Simulation, Numerical Analysis, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/b9fd8d249f37d6bff61a0a3edddfd50ed438dfb0

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Citations in the corpus

Time-fractional Diffusion of Distributed Order (2007, background): “Finally the Laplace inversion yields, see and compare [30, 51],”
A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation (2014, unknown): “The main purpose of this article is to propose an ε-approximate solution by using a reproducing kernel collocation method for the following modified anomalous subdiffusion equation with a linear source term in a finite domain [18, 21]: ∂u(x, t) ∂t = ( μ ∂1−α ∂t1−α + ν ∂ 1−β ∂x1−β ) ∂(2)u(x, t) ∂x2 +”
Numerical analysis for distributed-order differential equations (2009, background): “(1) We draw particular attention to the papers by [2, 3], [4, 5, 6, 7, 8], [19], [26], [25], and the paper by [1] which show the range of potential applications Gesellschaft für Numerische Simulation mbH, Am Gaußberg 2, 38114 Braunschweig, Germany Mathematics Department, University of Chester, CH1 4”
Stochastic model for ultraslow diffusion (2006, unknown): “An application where ψA(i Dx ) = ∂2/∂x2 and ρ(dβ) consists of two atoms at 0 < β1 < β2 < 1 is considered in [48], Section 4.”
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems (2016, unknown): “[2]-[4], [21], [27] and references therein).”
Distributed order calculus and equations of ultraslow diffusion (2007, background): “A number of recent publications by physicists (see [3, 4, 5, 25, 38] and references there) is devoted to the case where the mean square displacement has a logarithmic growth.”
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density (2013, methodology): “In [7], [10], and [35], integro-differential equations with distributed order temporal derivatives were treated and employed for kinetic description of anomalous diffusion and relaxation phenomena.”
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations (2014, unknown): “, [3]-[4], [15], [17], [21] and the references therein).”
BOUNDARY VALUE PROBLEMS FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATION OF DISTRIBUTED ORDER (2009, background): “[1]-[3], [20], [23] and references there) the sub-diffusion processes with the mean square displacement with a logarithmic growth have been introduced.”