Hacettepe Journal of Mathematics and Statistics 2651-477X 2651-477X Hacettepe University 10.15672/hujms.1285069 Mathematical Sciences Matematik Unique recovery of the initial state of distributed order time fractional diffusion equation https://orcid.org/0009-0008-8095-3245 Liu Hui Ningbo University https://orcid.org/0000-0002-5961-7211 Li Zhiyuan Ningbo University https://orcid.org/0000-0001-9024-8242 Ruan Zhousheng East China University of Technology 12 28 2024 53 6 1560 1574 04 18 2023 11 18 2023 Copyright © 2002, Hacettepe Journal of Mathematics and Statistics 2002 Hacettepe Journal of Mathematics and Statistics

We use Phragmén-Lindelöf-Liouville argument to prove the uniqueness for the determining the initial state of solution for the time fractional diffusion equation with distributed order derivative. Several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

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