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A mathematical model of the one-dimensional thermoelasticity problem was established based on the new thermoelasticity theory. We considered the symmetry of the material, and the fractional-order thermoelasticity control equation was given. Subsequently, the control equations were solved and analyzed using the Laplace transform and its inverse transform. This study examined the effects of fractional-order parameters, time, two thermal relaxation times, and the speed of movement of the heat source on the displacement, temperature, and stress distribution patterns in the rod.<\/jats:p>","DOI":"10.3390\/sym16060666","type":"journal-article","created":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T13:32:55Z","timestamp":1716903175000},"page":"666","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Thermoelastic Dynamic Response of a Rod Due to a Moving Heat Source under the Fractional-Order Thermoelasticity Theory"],"prefix":"10.3390","volume":"16","author":[{"given":"Fengjun","family":"Liu","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Henan University of Science and Technology, Luoyang 471023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengjie","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Henan University of Science and Technology, Luoyang 471023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1509-0451","authenticated-orcid":false,"given":"Ying","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Henan University of Science and Technology, Luoyang 471023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1063\/1.1722351","article-title":"Thermoelasticity and irreversible thermodynamics","volume":"27","author":"Biot","year":"1956","journal-title":"J. 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