A regularization for time-fractional backward heat conduction problem with inhomogeneous source function

Recently, Nair and Danumjaya [A new regularization for time-fractional backward heat conduction problem. J. Inverse Ill-Posed Probl. 2024;32:41–56] introduced a new regularization method for the homogeneous time-fractional backward heat conduction problem (TFBHCP) in a one-dimensional space variable. This paper extends that analysis to a more general setting of an inhomogeneous time-fractional heat equation with higher-dimensional state variables and a general elliptic operator. An error analysis is carried out for this extended regularization method, proving that the resulting error estimate is order-optimal under a specified source condition when the regularization parameter is chosen appropriately. Finally, numerical experiments are presented to illustrate and validate the theoretical results.