{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:21:52Z","timestamp":1758270112413},"reference-count":30,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"4","license":[{"start":{"date-parts":[[2016,12,1]],"date-time":"2016-12-01T00:00:00Z","timestamp":1480550400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p> A new, state space, non-integer order model for the heat transfer process is presented. The proposed model is based on a Feller semigroup one, the derivative with respect to time is expressed by the non-integer order Caputo operator, and the derivative with respect to length is described by the non-integer order Riesz operator. Elementary properties of the state operator are proven and a formula for the step response of the system is also given. The proposed model is applied to the modeling of temperature distribution in a one dimensional plant. Results of experiments show that the proposed model is more accurate than the analogical integer order model in the sense of the MSE cost function.<\/jats:p>","DOI":"10.1515\/amcs-2016-0052","type":"journal-article","created":{"date-parts":[[2017,1,19]],"date-time":"2017-01-19T12:27:11Z","timestamp":1484828831000},"page":"749-756","source":"Crossref","is-referenced-by-count":21,"title":["Modeling heat distribution with the use of a non-integer order, state space model"],"prefix":"10.61822","volume":"26","author":[{"given":"Krzysztof","family":"Oprz\u0119dkiewicz","sequence":"first","affiliation":[{"name":"Department of Automatics and Biomedical Engineering AGH University of Science and Technology, al. A. Mickiewicza 30, 30-079 Krak\u00f3w, Poland"}]},{"given":"Edyta","family":"Gawin","sequence":"additional","affiliation":[{"name":"Department of Computer Sciences High Vocational School in Tarn\u00f3w, al. 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