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Research Article | Open Access

Inversion formulas for space-fractional Bessel heat diffusion through Tikhonov regularization

Department of Mathematics, College of Sciences, King Saud University, P. O Box 2455 Riyadh 11451, Saudi Arabia
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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.

Keywords

Weierstrass transformbest approximationHankel transformreproducing kernelTikhonov regularization
CLC number: 44A15, 46E22, 35K05

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 20826-20842
DOI: 10.3934/math.20241013

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Cite this article:
Bouzeffour F. Inversion formulas for space-fractional Bessel heat diffusion through Tikhonov regularization. AIMS Mathematics, 2024, 9(8): 20826-20842. https://doi.org/10.3934/math.20241013

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Received: 05 May 2024
Revised: 14 June 2024
Accepted: 18 June 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)