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The effects of fractional order and relaxation coefficients are analyzed. Explicit solution of the equation was given in an example that generalizes several cases and then reweighed graphically in particular known cases. The applied approach is simple and effective in terms of calculation time, efficient in terms of efficiency and simplicity. <\/jats:p>","DOI":"10.1142\/s179396232541020x","type":"journal-article","created":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T10:13:31Z","timestamp":1747995211000},"source":"Crossref","is-referenced-by-count":0,"title":["Analytical solution for aqueous polymer solutions equation with a fractional time derivative by Adomian decomposition method"],"prefix":"10.1142","volume":"16","author":[{"given":"Slimane","family":"Azoug","sequence":"first","affiliation":[{"name":"AMNEDP, Faculty of Mathematics, University of Science and Technology Houari Boumediene (USTHB), Algiers, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1424","authenticated-orcid":false,"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India"},{"name":"Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey"},{"name":"Department of Computer Engineering, Biruni University, 34010 Topkap\u0131, Istanbul, Turkey"},{"name":"Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138, Nicosia\/Mersin 10 \u2013 Turkey"},{"name":"Applied Science Research Center, Applied Science Private University, Amman, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lahcen","family":"Azrar","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, King AbdulAziz University, Jeddah, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,7,2]]},"reference":[{"key":"S179396232541020XBIB001","doi-asserted-by":"publisher","DOI":"10.1115\/1.3625016"},{"key":"S179396232541020XBIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01084613"},{"key":"S179396232541020XBIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2008.03.005"},{"key":"S179396232541020XBIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.08.011"},{"key":"S179396232541020XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2007.03.019"},{"key":"S179396232541020XBIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-020-1110-3"},{"issue":"2","key":"S179396232541020XBIB007","first-page":"86","volume":"15","author":"He J.","year":"1999","journal-title":"Bull. 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