TY - JOUR
T1 - A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation
AU - Shuping Yang & Xiangtuan Xiong
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 386
EP - 408
PY - 2019
DA - 2019/03
SN - 9
DO - http://doi.org/10.4208/eajam.090918.030119 
UR - https://global-sci.org/intro/article_detail/eajam/13089.html
KW - Inverse source problem, fractional Tikhonov regularisation method, error estimate.
AB - <p style="text-align: justify;">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.</p>