Work

A Novel Approach to the Fractional Laplacian via Generalized Spherical Means

Year: 2024

Type: article

Abstract: Although at least ten equivalent definitions of the fractional Laplacian exist in unbounded domains, we introduce an additional equivalent definition based on the generalized spherical mean-value operator—a Fourier multiplier operator involving the normalized Bessel function. Specifically, we demonstrate that this new definition allows us to reduce any n-dimensional fractional Laplacian to a one-dimensional operator, which simplifies computation and enhances efficiency. We propose two methods for computing the generalized spherical means of a given function: one by solving standard wave equations and the other by solving Darboux’s equations.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8110618

Author: Fethi Bouzeffour

Institution: King Saud University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

Funder: King Saud University