{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:17:05Z","timestamp":1760149025507,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T00:00:00Z","timestamp":1687996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11871064","11571300"],"award-info":[{"award-number":["11871064","11571300"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we investigate the concept of regional enlarged observability (ReEnOb) for fractional differential equations (FDEs) with the Hilfer derivative. To proceed this, we develop an approach based on the Hilbert uniqueness method (HUM). We mainly reconstruct the initial state \u03bd01 on an internal subregion \u03c9 from the whole domain \u03a9 with knowledge of the initial information of the system and some given measurements. This approach shows that it is possible to obtain the desired state between two profiles in some selective internal subregions. Our findings develop and generalize some known results. Finally, we give two examples to support our theoretical results.<\/jats:p>","DOI":"10.3390\/axioms12070648","type":"journal-article","created":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T01:14:12Z","timestamp":1688087652000},"page":"648","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Regional Enlarged Observability for Hilfer Fractional Differential Equations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9539-7594","authenticated-orcid":false,"given":"Abu Bakr","family":"Elbukhari","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China"},{"name":"Department of Mathematics, Faculty of Education, University of Khartoum, Khartoum, Omdurman 406, Sudan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6238-771X","authenticated-orcid":false,"given":"Zhenbin","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6941-9470","authenticated-orcid":false,"given":"Gang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"ref_1","unstructured":"Petr\u00e1\u0161, I. 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