{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T06:20:20Z","timestamp":1762410020713,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T00:00:00Z","timestamp":1649635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007847","name":"Natural Science Foundation of Jilin Province","doi-asserted-by":"publisher","award":["No. 20200201274JC"],"award-info":[{"award-number":["No. 20200201274JC"]}],"id":[{"id":"10.13039\/100007847","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.11201095"],"award-info":[{"award-number":["No.11201095"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postdoctoral research startup foundation of Heilongjiang","award":["No.LBH-Q14044"],"award-info":[{"award-number":["No.LBH-Q14044"]}]},{"name":"Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province","award":["No. LC201502"],"award-info":[{"award-number":["No. LC201502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we investigate the topological structure of the solution set to a fractional differential inclusion with delay defined on the half-line. We first prove that the solution set to the inclusion is an R\u03b4-set on compact intervals. Then, by means of the inverse limit method, we generalize our results to noncompact intervals. Moreover, under convex and nonconvex conditions, an R\u03b4-property solution set is obtained for some nonlocal problems, where the nonlocal function is set-valued. Further, we study the symmetry of the solution set under some conditions.<\/jats:p>","DOI":"10.3390\/sym14040792","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T22:48:45Z","timestamp":1649803725000},"page":"792","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Topological Structure of Solution Set to a Fractional Differential Inclusion Problem with Delay"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0995-5164","authenticated-orcid":false,"given":"Shanshan","family":"Gao","sequence":"first","affiliation":[{"name":"College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Changchun University of Finance and Economics, Changchun 130000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7965-1348","authenticated-orcid":false,"given":"Bin","family":"Ge","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"730","DOI":"10.2307\/1968963","article-title":"Le correspondant topologique de l\u2019unicit dans la thorie des quations diffrentielles","volume":"43","author":"Aronszajn","year":"1942","journal-title":"Ann. 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