@article{Halouani2024, 
author = {Borhen Halouani and Fethi Bouzeffour},
title = {On the fractional Laplace-Bessel operator},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {21524-21537},
keywords = {Laplace-Bessel operator, fractional calculus, Bessel function},
url = {https://www.sciopen.com/article/10.3934/math.20241045},
doi = {10.3934/math.20241045},
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.}
}