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The Fractional Laplacian

, 2016
The fractional Laplacian in one dimension Random walkers with constant steps Ordinary diffusion Random jumpers Central limit theorem and stable distributions Power-law probability jump lengths A principal-value integral Wires and springs The fractional ...
C. Pozrikidis
semanticscholar   +2 more sources

Modeling viscoacoustic wave propagation using a new spatial variable-order fractional Laplacian wave equation

Geophysics, 2021
We have developed a new time-domain viscoacoustic wave equation for simulating wave propagation in anelastic media. The new wave equation is derived by inserting the complex-valued phase velocity described by the Kjartansson attenuation model into the ...
X. Mu, Jianping Huang, L. Wen, S. Zhuang
semanticscholar   +1 more source

Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain

Applied Mathematics Letters, 2021
This paper proposes a fast and efficient spectral-Galerkin method for the nonlinear complex Ginzburg-Landau equation involving the fractional Laplacian in R d . By employing the Fourier-like bi-orthogonal mapped Chebyshev function as basis functions, the
Pengde Wang
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On the Generalized Fractional Laplacian

Fractional Calculus and Applied Analysis, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Schrödinger Equations with Fractional Laplacians

Applied Mathematics & Optimization, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hu, Y., Kallianpur, G.
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Asymptotic behaviours of solution to Caputo–Hadamard fractional partial differential equation with fractional Laplacian

International Journal of Computational Mathematics, 2020
In this paper, we study the asymptotic behaviours of solution to time–space fractional diffusion equation, where the time derivative with order α is in the sense of Caputo–Hadamard and the spatial derivative is in the sense of fractional Laplacian ...
Changpin Li, Zhiqiang Li
semanticscholar   +1 more source

Matrix Transfer Technique for Anomalous Diffusion Equation Involving Fractional Laplacian

Applied Numerical Mathematics, 2021
The fractional Laplacian, ( − △ ) s , s ∈ ( 0 , 1 ) , appears in a wide range of physical systems, including Levy flights, some stochastic interfaces, and theoretical physics in connection to the problem of stability of the matter.
Minling Zheng   +3 more
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Radial symmetry of standing waves for nonlinear fractional Laplacian Hardy-Schrödinger systems

Applied Mathematics Letters, 2020
In this paper, by applying the direct method of moving planes, the authors study the radial symmetry of standing waves for nonlinear fractional Laplacian Schrodinger systems with Hardy potential. Firstly, under the condition of infinite decay, the radial
Guotao Wang, Xueyan Ren
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BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS

Stochastics and Dynamics, 2005
By making use of the reflected α-stable process on a closed domain of ℝn and its killed subprocess on part of the domain, in this paper we study the boundary value problem for the Schrödinger type equation of a fractional Laplacian. The boundary condition is imposed partly follow Dirichlet condition and partly follow Neuman condition.
Guan, Qing-Yang, Ma, Zhi-Ming
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Fractional Brownian motion via fractional Laplacian

Statistics & Probability Letters, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bojdecki, Tomasz, Gorostiza, Luis G.
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