A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation

Abstract

The ill-posed problems of the identification of unknown source terms in a time-fractional radial heat conduction problem are studied. To overcome the difficulties caused by the ill-posedness, a fractional Tikhonov regularisation method is proposed. Employing Mittag-Leffler function, we obtain error estimates under a priori and a posteriori regularisation parameter choices. In the last situation, the Morozov discrepancy principle is also used. Numerical examples show that the method is a stable and effective tool in the reconstruction of smooth and non-smooth source terms and, generally, outperforms the classical Tikhonov regularisation.