{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:56:50Z","timestamp":1760057810195,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T00:00:00Z","timestamp":1740182400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>The thermistor model captures the complex interaction between heat dissipation, electrical current conduction, and Joule heat generation. Our research examines the diverse properties and implications of employing fractional calculus in the analysis with a focus on fixed-point principles. This paper addresses the existence and uniqueness of solutions to a variable order Caputo fractional thermistor problem by applying Schauder\u2019s fixed-point theorem.<\/jats:p>","DOI":"10.3390\/fractalfract9030139","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T05:36:47Z","timestamp":1740375407000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence of Solutions to the Variable Order Caputo Fractional Thermistor Problem"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8149-4633","authenticated-orcid":false,"given":"John R.","family":"Graef","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2237-2713","authenticated-orcid":false,"given":"Kadda","family":"Maazouz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ibn Khaldoun, Tiaret 14000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0984-0159","authenticated-orcid":false,"given":"Sandra","family":"Pinelas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade de Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8893-1085","authenticated-orcid":false,"given":"Zineb","family":"Bellabes","sequence":"additional","affiliation":[{"name":"Laboratory of Fundamental and Applied Mathematics (LMFAO), University of Oran 1, Oran 31000, Algeria"}]},{"given":"Naima","family":"Boussekkine","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Relizane University, Relizane 48000, Algeria"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1017\/S0956792500001686","article-title":"A nonlocal thermistor problem","volume":"6","author":"Allegretto","year":"1995","journal-title":"Europ. 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