A new definition of the fractional Laplacian

Details A new definition of the fractional Laplacian A new definition of the fractional Laplacian

2002-09-18

arxiv.org/abs/cs/0209020v1

Computer Science

Numerical Analysis

This study is carred out with the ongoing project of "mathematical and numerical modelling of medical ultasound wave propagati

Scientific paper

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.

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