{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T08:56:13Z","timestamp":1767084973800,"version":"build-2065373602"},"reference-count":73,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,26]],"date-time":"2025-01-26T00:00:00Z","timestamp":1737849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shandong Province of China","award":["ZR2022AM015"],"award-info":[{"award-number":["ZR2022AM015"]}]},{"name":"ARC Discovery Project Grant","award":["ZR2022AM015"],"award-info":[{"award-number":["ZR2022AM015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we focus on the existence and asymptotic estimates of the maximal and minimal solutions for a coupled tempered fractional differential system with different orders. By introducing an order reduction technique and some new growth conditions, we establish some new results on the existence of positive extremal solutions for the tempered fractional differential system, meanwhile, we also obtain the asymptotic estimate of the positive extreme solution by an iterative technique, which possesses a sharp asymptotic estimate. In particular, the iterative sequences converging to maximal and minimal solutions starting from two known initial values are easy to compute. Moreover, the weight function \u210fi is allowed to have an infinite number of singular points in [0,1].<\/jats:p>","DOI":"10.3390\/axioms14020092","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T08:57:48Z","timestamp":1738054668000},"page":"92","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Existence and Asymptotic Estimates of the Maximal and Minimal Solutions for a Coupled Tempered Fractional Differential System with Different Orders"],"prefix":"10.3390","volume":"14","author":[{"given":"Peng","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9250-6823","authenticated-orcid":false,"given":"Xinguang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, China"},{"name":"Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lishuang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongsheng","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1028-1785","authenticated-orcid":false,"given":"Yonghong","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1186\/s13661-019-1228-7","article-title":"A singular fractional Kelvin-Voigt model involving a nonlinear operator and their convergence properties","volume":"2019","author":"He","year":"2019","journal-title":"Bound. 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