{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:14:37Z","timestamp":1760148877832,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T00:00:00Z","timestamp":1686873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"],"award-info":[{"award-number":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"]}]},{"name":"Scientific Research Foundation of Northwest University","award":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"],"award-info":[{"award-number":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"]}]},{"name":"Agencia Estatal de Investigaci\u00f3n (AEI) of Spain","award":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"],"award-info":[{"award-number":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"]}]},{"name":"European Community Regional Development Fund (FEDER) and by Xunta de Galicia","award":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"],"award-info":[{"award-number":["11901448","11871022","PID2020-113275GB-I00","ED431C 2019\/02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The long-term behavior of the weak solution of a fractional delayed reaction\u2013diffusion equation with a generalized Caputo derivative is investigated. By using the classic Galerkin approximation method and comparison principal, the existence and uniqueness of the solution is proved in the sense of weak solution. In addition, the global attracting set of the considered system is obtained, with the help of the Sobolev embedding theorem and Halanay inequality.<\/jats:p>","DOI":"10.3390\/e25060950","type":"journal-article","created":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T03:04:40Z","timestamp":1687143880000},"page":"950","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamics of Fractional Delayed Reaction-Diffusion Equations"],"prefix":"10.3390","volume":"25","author":[{"given":"Linfang","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8202-6578","authenticated-orcid":false,"given":"Juan J.","family":"Nieto","sequence":"additional","affiliation":[{"name":"Departamento de An\u00e1lise Matem\u00e1tica, Estat\u00edstica e Optimizaci\u00f3n, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1137\/17M1160318","article-title":"A Generalized Definition of Caputo Derivatives and Its Application to Fractional ODEs","volume":"50","author":"Li","year":"2018","journal-title":"SIAM J. 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