{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T12:30:21Z","timestamp":1772368221340,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T00:00:00Z","timestamp":1558137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The time-fractional heat conduction equation follows from the law of conservation of energy and the corresponding time-nonlocal extension of the Fourier law with the \u201clong-tail\u201d power kernel. The time-fractional heat conduction equation with the Caputo derivative is solved for an infinite plane with two external half-infinite slits with the prescribed heat flux across their surfaces. The integral transform technique is used. The solution is obtained in the form of integrals with integrand being the Mittag\u2013Leffler function. A graphical representation of numerical results is given.<\/jats:p>","DOI":"10.3390\/sym11050689","type":"journal-article","created":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T11:05:07Z","timestamp":1558350307000},"page":"689","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7492-5394","authenticated-orcid":false,"given":"Yuriy","family":"Povstenko","sequence":"first","affiliation":[{"name":"Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Armii Krajowej 13\/15, 42-200 Czestochowa, Poland"}]},{"given":"Tamara","family":"Kyrylych","sequence":"additional","affiliation":[{"name":"Department of Law, Administration and Management, Jan Dlugosz University in Czestochowa, Zbierskiego 2\/4, 42-200 Czestochowa, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF00281373","article-title":"A general theory of heat conduction with finite wave speeds","volume":"31","author":"Gurtin","year":"1968","journal-title":"Arch. 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