Results 271 to 280 of about 416,500 (289)

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   +3 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

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

Existence of solution for a singular fractional Laplacian problem with variable exponents and indefinite weights

, 2020
In this paper, we consider a class of fractional Laplacian problems of the form: where is a bounded domain and is the fractional -Laplacian. We assume that λ is a nonnegative parameter and is a continuous function.
R. Chammem, A. Ghanmi, A. Sahbani
semanticscholar   +1 more source

Difference between Riesz derivative and fractional Laplacian on the proper subset of ℝ

Fractional Calculus and Applied Analysis, 2021
In general, the Riesz derivative and the fractional Laplacian are equivalent on ℝ. But they generally are not equivalent with each other on any proper subset of ℝ. In this paper, we focus on the difference between them on the proper subset of ℝ.
Caiyu Jiao, A. Khaliq, Changpin Li, Hexiang Wang   +3 more
semanticscholar   +1 more source

Distributed order fractional diffusion equation with fractional Laplacian in axisymmetric cylindrical configuration

Communications in nonlinear science & numerical simulation, 2022
A. Ansari, M. Derakhshan, Hassan Askari
semanticscholar   +1 more source

On spectral polar fractional Laplacian

Mathematics and Computers in Simulation, 2022
A. Ansari, M. Derakhshan
semanticscholar   +1 more source

The Blow-Up and Global Existence of Solution to Caputo–Hadamard Fractional Partial Differential Equation with Fractional Laplacian

Journal of nonlinear science, 2021
Changpin Li, Zhiqiang Li
semanticscholar   +1 more source

Efficient modeling of wave propagation in a vertical transversely isotropic attenuative medium based on fractional Laplacian

Geophysics, 2019
To efficiently simulate wave propagation in a vertical transversely isotropic (VTI) attenuative medium, we have developed a viscoelastic VTI wave equation based on fractional Laplacian operators under the assumption of weak attenuation ([Formula: see ...
T. Zhu, Tong Bai
semanticscholar   +1 more source

An Introduction to the Fractional Laplacian

2016
We introduce here some preliminary notions on the fractional Laplacian and on fractional Sobolev spaces. The definition and equivalent representations for the fractional Laplacian are introduced and the constant that appears in this definition is explicitly computed.
Claudia Bucur, Enrico Valdinoci
openaire   +2 more sources