A new definition of the fractional Laplacian
Numerical Analysis
2025-10-20 v1 Computational Engineering, Finance, and Science
Numerical Analysis
Abstract
It is noted that the standard definition of the fractional Laplacian leads to a hyper-singular convolution integral and is also obscure about how to implement the boundary conditions. This purpose of this note is to introduce a new definition of the fractional Laplacian to overcome these major drawbacks.
Cite
@article{arxiv.cs/0209020,
title = {A new definition of the fractional Laplacian},
author = {W. Chen},
journal= {arXiv preprint arXiv:cs/0209020},
year = {2025}
}
Comments
This study is carred out with the ongoing project of "mathematical and numerical modelling of medical ultasound wave propagation" sponsored by the Simula Research Laboratory