{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:41:13Z","timestamp":1760236873886,"version":"build-2065373602"},"reference-count":76,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,30]],"date-time":"2021-12-30T00:00:00Z","timestamp":1640822400000},"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>In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R&lt;r&lt;\u03c1. The stress intensity factor is calculated as a function of the order of time-derivative, time, and the size of a circular ring and is presented graphically.<\/jats:p>","DOI":"10.3390\/e24010070","type":"journal-article","created":{"date-parts":[[2021,12,30]],"date-time":"2021-12-30T21:41:21Z","timestamp":1640900481000},"page":"70","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An External Circular Crack in an Infinite Solid under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity"],"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1486-6572","authenticated-orcid":false,"given":"Bo\u017cena","family":"Wo\u017ana-Szcze\u015bniak","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. 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Armii Krajowej 13\/15, 42-200 Czestochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrzej","family":"Yatsko","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Civil Engineering, Environmental and Geodesic Sciences, Koszalin University of Technology, \u015aniadeckich 2, 75-453 Koszalin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/0021-8928(59)90062-0","article-title":"Elastic equilibrium in an infinite body weakened by an external circular crack","volume":"23","author":"Uflyand","year":"1959","journal-title":"J. Appl. Math. Mech."},{"key":"ref_2","unstructured":"Uflyand, Y.S. (1967). Integral Transforms in Problem of the Theory of Elasticity, Nauka. 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