@article{Bouzeffour2024, 
author = {Fethi Bouzeffour},
title = {Inversion formulas for space-fractional Bessel heat diffusion through Tikhonov regularization},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {20826-20842},
keywords = {Weierstrass transform, best approximation, Hankel transform, reproducing kernel, Tikhonov regularization},
url = {https://www.sciopen.com/article/10.3934/math.20241013},
doi = {10.3934/math.20241013},
abstract = {This article explores the generalized Gauss-Weierstrass transform associated with the space-fractional Bessel diffusion equation. Explicit inversion formulae for this transform are developed using best approximation methods and reproducing kernel theory. To address the inherent ill-posedness of this transform, Tikhonov regularization is implemented. Furthermore, the convergence rate of the regularized solutions is rigorously established.}
}