A Regularization for Time-Fractional Backward Heat Conduction Problem with Inhomogeneous Source Function
<|reference_start|>A Regularization for Time-Fractional Backward Heat Conduction Problem with Inhomogeneous Source Function: 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.<|reference_end|>
@article{alavani2024a,
    title={A Regularization for Time-Fractional Backward Heat Conduction Problem
  with Inhomogeneous Source Function},
    author={Vighnesh V. Alavani, P. Danumjaya, M.Thamban Nair},
    journal={arXiv preprint arXiv:2405.18074},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.18074},
    primaryClass={math.AP cs.NA math.NA}
}