{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:05:26Z","timestamp":1761581126699,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T00:00:00Z","timestamp":1380240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion (0&lt; r &lt; R)                                                   and a matrix (R &lt;  r &lt; \u221e)     being in perfect thermal contact at r = R     is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order    0 &lt; a \u2264 2 and 0 &lt; \u03b2 \u2264 2,     respectively. The Laplace transform with respect to time is used. The approximate solution valid for small values of time is obtained in terms of the Mittag-Leffler, Wright, and Mainardi functions.<\/jats:p>","DOI":"10.3390\/e15104122","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T12:42:41Z","timestamp":1380285761000},"page":"4122-4133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7492-5394","authenticated-orcid":false,"given":"Yuriy","family":"Povstenko","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Computer Science, Jan D\u0142ugosz University in Cz\u0119stochowa, Armii Krajowej 13\/15, Cz\u0119stochowa 42-200, Poland"},{"name":"Department of Computer Science, European University of Informatics and Economics (EWSIE) Bia\u0142ostocka 22, Warsaw 03-741, Poland\u00a0"}]}],"member":"1968","published-online":{"date-parts":[[2013,9,27]]},"reference":[{"key":"ref_1","first-page":"35","article-title":"A note on the non-classical heat condition","volume":"13","author":"Petrov","year":"1982","journal-title":"Bulg. 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