A Regularization for Time-Fractional Backward Heat Conduction Problem with Inhomogeneous Source Function

Abstract

Recently, Nair and Danumjaya (2023) introduced a new regularization method for the homogeneous time-fractional backward heat conduction problem (TFBHCP) in a one-dimensional space variable, for determining the initial value function. In this paper, the authors extend the analysis done in the above referred paper to a more general setting of an inhomogeneous time-fractional heat equation involving the higher dimensional state variables and a general elliptic operator. We carry out the analysis for the newly introduced regularization method for the TFBHCP providing optimal order error estimates under a source condition by choosing the regularization parameter appropriately, and also carry out numerical experiments illustrating the theoretical results.