{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:40:53Z","timestamp":1740156053425,"version":"3.37.3"},"reference-count":32,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,8]],"date-time":"2022-08-08T00:00:00Z","timestamp":1659916800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11961044"]},{"name":"Doctor Fund of Lan Zhou University of Technology"},{"name":"Natural Science Foundation of Gansu Province","award":["21JR7RA214"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"In this paper, the inverse problem for identifying the initial value of a time fractional nonhomogeneous diffusion equation in a columnar symmetric region is studied. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. The fractional Tikhonov regularization method is applied to solve this problem and obtain the regularization solution. The error estimations between the regularization solution and the exact solution are also obtained under the priori and the posteriori regularization parameter choice rules, respectively. Some examples are given to show this method\u2019s effectiveness.<\/jats:p>","DOI":"10.3390\/sym14081633","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T13:47:06Z","timestamp":1660139226000},"page":"1633","source":"Crossref","is-referenced-by-count":1,"title":["The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7597-3371","authenticated-orcid":false,"given":"Yong-Gang","family":"Chen","sequence":"first","affiliation":[{"name":"School of Science, China University of Petroleum, Qindao 266580, China"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou 730050, China"}]},{"given":"Xiao-Xiao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou 730050, China"}]},{"given":"Dun-Gang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou 730050, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.matcom.2006.09.005","article-title":"A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat conduction problem","volume":"75","author":"Cheng","year":"2007","journal-title":"Math. 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