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Fractional-order dependent Radial basis functions meshless methods for the integral fractional Laplacian
Zhaopeng Hao, Zhiqiang Cai, Zhongqiang Zhang
We study the numerical evaluation of the integral fractional Laplacian and its application in solving fractional diffusion equations. We derive a pseudo-spectral formula for the in…
A simple and fast finite difference method for the integral fractional Laplacian of variable order
Zhaopeng Hao, Siyuan Shi, Zhongqiang Zhang +1
For the fractional Laplacian of variable order, an efficient and accurate numerical evaluation in multi-dimension is a challenge for the nature of a singular integral. We propose a…
On spectral Petrov-Galerkin method for solving fractional initial value problems in weighted Sobolev space
Shengyue Li, Wanrong Cao, Zhaopeng Hao
In this paper, we investigate a spectral Petrov-Galerkin method for fractional initial value problems. Singularities of the solution at the origin inherited from the weakly singula…
Regularity and spectral methods for two-sided fractional diffusion equations with a low-order term
Zhaopeng Hao, Guang Lin, Zhongqiang Zhang
We study regularity and numerical methods for two-sided fractional diffusion equations with a lower-order term. We show that the regularity of the solution in weighted Sobolev spac…