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A Fourier Method for the Fractional Diffusion Equation Describing Sub-Diffusion [PDF]

open access: yesJournal of Computational Physics, 2007
In this paper, a fractional partial differential equation (FPDE) describing sub-diffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented.
Chang-Ming Chen, Fawang Liu, Vo Anh
exaly   +2 more sources
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On a Fractional Diffusion Equation with Moving Control

SIAM Journal on Control and Optimization, 2022
This article considers a one-dimensional fractional parabolic equation, which may serve as a mathematical model for anomalous diffusion phenomena. It is known that, if the support of the control is fixed, this equation is not even spectrally controllable.
Sorin Micu, Constantin Nita
openaire   +3 more sources

On a fractional reaction–diffusion equation

Zeitschrift für angewandte Mathematik und Physik, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
de Andrade, Bruno, Viana, Arlúcio
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Fractional diffusion and fractional heat equation

Advances in Applied Probability, 2000
This paper introduces a fractional heat equation, where the diffusion operator is the composition of the Bessel and Riesz potentials. Sharp bounds are obtained for the variance of the spatial and temporal increments of the solution. These bounds establish the degree of singularity of the sample paths of the solution.
Angulo, J. M.   +3 more
openaire   +1 more source

Identify the fractional order and diffusion coefficient in a fractional diffusion wave equation

Journal of Computational and Applied Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiongbin Yan, Yuan-Xiang Zhang, Ting Wei
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Multigrid method for fractional diffusion equations

Journal of Computational Physics, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong-Kui Pang, Hai-Wei Sun
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Apriori estimates for fractional diffusion equation

Optimization Letters, 2018
We derive 2([0, ) ; /2 (ℝ )), ∈[1, 2), apriori estimate for solutions to the fractional or anomalous diffusion equation using a generalization of the Leibnitz rule for the fractional Laplacean. The equation models a wide range of physical phenomena and, in particular, it is a linearized variant of the fractional porous media equation.
Burazin, Krešimir, Mitrović, Darko
openaire   +3 more sources

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