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

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 transform
• best approximation
• hankel transform
• reproducing kernel
• tikhonov regularization