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Research Article | Open Access

On the fractional Laplace-Bessel operator

Borhen Halouani( ), Fethi Bouzeffour
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Abstract

In this paper, we propose a novel approach to the fractional power of the Laplace-Bessel operator Δν, defined as

Δν=∑i=1n∂2∂xi2+νixi∂∂xi,νi≥0.

The fractional power of this operator is introduced as a pseudo-differential operator through the multi-dimensional Bessel transform. Our primary contributions encompass a normalized singular integral representation, Bochner subordination, and intertwining relations.

Keywords

Laplace-Bessel operatorfractional calculusBessel function
CLC number: 43A32, 44A15

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 21524-21537
DOI: 10.3934/math.20241045

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Cite this article:
Halouani B, Bouzeffour F. On the fractional Laplace-Bessel operator. AIMS Mathematics, 2024, 9(8): 21524-21537. https://doi.org/10.3934/math.20241045

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Received: 24 March 2024
Revised: 11 May 2024
Accepted: 16 May 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)