@Article{EAJAM-9-386, author = {}, title = {A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {2}, pages = {386--408}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090918.030119 }, url = {http://global-sci.org/intro/article_detail/eajam/13089.html} }