Fractional diffusion equations involving external forces in the higher dimensional case

Zou, Fu; Ren, Fu-Yao; Qiu, Weiyuan

doi:10.1016/j.chaos.2003.12.082

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…Remark 1: The fundamental solutions and the asymptotic solutions of Eq. ( 2) (containing its special cases) have been considered in many previous works [10,16,[28][29][30][31][32][33][34]. In the following section we will consider two types of asymptotic behaviors of the jump PDF ψ(x, t) in the Fourier-Laplace space and derive the corresponding space-time FDEs.…”

Section: The Space-time Fractional Diffusion Equationmentioning

confidence: 99%

Space–time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

Shi

Mao

et al. 2013

Physica A: Statistical Mechanics and its Applications

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In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are discussed. The corresponding fractional diffusion equations are derived from the given asymptotic behaviors. Corresponding to the asymptotic behaviors of the joint probability density function in the Fourier-Laplace space, the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed.

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Section: The Space-time Fractional Diffusion Equationmentioning

confidence: 99%

Space–time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

Shi

Mao

et al. 2013

Physica A: Statistical Mechanics and its Applications

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“…Agrawal [16] presented fundamental solutions for a FDWE where the diffusion equation contained a fourth-order space derivative and a fractional order time derivative. Zou et al [17] considered a fractional diffusion equation of higher dimension to describe anomalous diffusion processes involving external force fields by using Giona and Roman's heuristic argument. Hilfer [18] proposed the closed form solution of a fractional diffusion problem in terms of H-functions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of an axis-symmetric fractional diffusion-wave problem

Özdemir

Agrawal

Karadeniz

et al. 2009

J. Phys. A: Math. Theor.

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This paper presents an axis-symmetric fractional diffusion-wave problem which is considered in polar coordinates. The dynamic characteristics of the system are described with a partial fractional differential equation in terms of the Riemann–Liouville fractional derivative. This continuum problem is reduced to a countable infinite problem by using the method of separation of variables. In this way, the closed form solution of the problem is obtained. The Grünwald–Letnikov approach is applied to take a numerical evaluation. The compatibility and effectiveness of this approach are realized by some simulation results which are obtained by a MATLAB program. It can be seen that the analytical and numerical solutions overlap.

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