{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T05:11:24Z","timestamp":1762060284333,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T00:00:00Z","timestamp":1658275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The axisymmetric time-fractional diffusion equation with mass absorption is studied in a circle under the time-harmonic Dirichlet boundary condition. The Caputo derivative of the order 0&lt;\u03b1\u22642 is used. The investigated equation can be considered as the time-fractional generalization of the bioheat equation and the Klein\u2013Gordon equation. Different formulations of the problem for integer values of the time-derivatives \u03b1=1 and \u03b1=2 are also discussed. The integral transform technique is employed. The outcomes of numerical calculations are illustrated graphically for different values of the parameters.<\/jats:p>","DOI":"10.3390\/e24071002","type":"journal-article","created":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T11:22:24Z","timestamp":1658316144000},"page":"1002","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Axisymmetric Fractional Diffusion with Mass Absorption in a Circle under Time-Harmonic Impact"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7492-5394","authenticated-orcid":false,"given":"Yuriy","family":"Povstenko","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13\/15, 42-200 Czestochowa, Poland"}]},{"given":"Tamara","family":"Kyrylych","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13\/15, 42-200 Czestochowa, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,20]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_2","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier."},{"key":"ref_3","unstructured":"Magin, R.L. (2006). Fractional Calculus in Bioengineering, Begell House Publishers, Inc."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mainardi, F. (2010). 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