A new definition of the fractional Laplacian
W. Chen
TL;DR
This paper introduces a new definition of the fractional Laplacian that addresses issues of hyper-singular integrals and boundary condition implementation present in the standard definition.
Contribution
The paper proposes a novel formulation of the fractional Laplacian to simplify its mathematical properties and improve boundary condition handling.
Findings
New definition reduces mathematical complexity.
Facilitates boundary condition implementation.
Addresses hyper-singularity issues.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Fractional Differential Equations Solutions · Numerical methods in inverse problems