{"id":"https://openalex.org/W4382786698","doi":"https://doi.org/10.3390/axioms12070648","title":"The Regional Enlarged Observability for Hilfer Fractional Differential Equations","display_name":"The Regional Enlarged Observability for Hilfer Fractional Differential Equations","publication_year":2023,"publication_date":"2023-06-29","ids":{"openalex":"https://openalex.org/W4382786698","doi":"https://doi.org/10.3390/axioms12070648"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12070648","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070648","pdf_url":"https://www.mdpi.com/2075-1680/12/7/648/pdf?version=1688022644","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/7/648/pdf?version=1688022644","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009612896","display_name":"Abu Bakr Elbukhari","orcid":"https://orcid.org/0000-0002-9539-7594"},"institutions":[{"id":"https://openalex.org/I150406212","display_name":"University of Khartoum","ror":"https://ror.org/02jbayz55","country_code":"SD","type":"education","lineage":["https://openalex.org/I150406212"]},{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN","SD"],"is_corresponding":true,"raw_author_name":"Abu Bakr Elbukhari","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, University of Khartoum, Khartoum, Omdurman 406, Sudan","School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China;"],"raw_orcid":"https://orcid.org/0000-0002-9539-7594","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, University of Khartoum, Khartoum, Omdurman 406, Sudan","institution_ids":["https://openalex.org/I150406212"]},{"raw_affiliation_string":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","institution_ids":["https://openalex.org/I78978612"]},{"raw_affiliation_string":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China;","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008227827","display_name":"Zhenbin Fan","orcid":"https://orcid.org/0000-0002-6238-771X"},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenbin Fan","raw_affiliation_strings":["School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China;"],"raw_orcid":"https://orcid.org/0000-0002-6238-771X","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","institution_ids":["https://openalex.org/I78978612"]},{"raw_affiliation_string":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China;","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100762004","display_name":"Gang Li","orcid":"https://orcid.org/0000-0002-6941-9470"},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Li","raw_affiliation_strings":["School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China;"],"raw_orcid":"https://orcid.org/0000-0002-6941-9470","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","institution_ids":["https://openalex.org/I78978612"]},{"raw_affiliation_string":"School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China;","institution_ids":["https://openalex.org/I78978612"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009612896"],"corresponding_institution_ids":["https://openalex.org/I150406212","https://openalex.org/I78978612"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5132,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64005953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"12","issue":"7","first_page":"648","last_page":"648"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.890643835067749},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7455308437347412},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5623626112937927},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5413084626197815},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5224679708480835},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46546459197998047},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4623490571975708},{"id":"https://openalex.org/keywords/hum","display_name":"Hum","score":0.445930540561676},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4448786973953247},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.41670000553131104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34042009711265564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10287860035896301},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08653324842453003}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.890643835067749},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7455308437347412},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5623626112937927},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5413084626197815},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5224679708480835},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46546459197998047},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4623490571975708},{"id":"https://openalex.org/C23161992","wikidata":"https://www.wikidata.org/wiki/Q2922301","display_name":"Hum","level":3,"score":0.445930540561676},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4448786973953247},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34042009711265564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10287860035896301},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08653324842453003},{"id":"https://openalex.org/C554144382","wikidata":"https://www.wikidata.org/wiki/Q213156","display_name":"Performance art","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12070648","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070648","pdf_url":"https://www.mdpi.com/2075-1680/12/7/648/pdf?version=1688022644","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d726a102553d41858ffa4c9bcd6323e2","is_oa":true,"landing_page_url":"https://doaj.org/article/d726a102553d41858ffa4c9bcd6323e2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 7, p 648 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/7/648/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12070648","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 7; Pages: 648","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12070648","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070648","pdf_url":"https://www.mdpi.com/2075-1680/12/7/648/pdf?version=1688022644","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G283714742","display_name":null,"funder_award_id":"11571300","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5544804194","display_name":null,"funder_award_id":"11871064","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382786698.pdf","grobid_xml":"https://content.openalex.org/works/W4382786698.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1981856088","https://openalex.org/W1991397548","https://openalex.org/W1997773011","https://openalex.org/W2073592294","https://openalex.org/W2121056813","https://openalex.org/W2154600465","https://openalex.org/W2395672747","https://openalex.org/W2473864312","https://openalex.org/W2479907525","https://openalex.org/W2625731045","https://openalex.org/W2784053309","https://openalex.org/W2809846016","https://openalex.org/W2902449853","https://openalex.org/W2921205466","https://openalex.org/W2947600952","https://openalex.org/W2969445909","https://openalex.org/W3104341805","https://openalex.org/W3105900447","https://openalex.org/W3120035920","https://openalex.org/W3147200511","https://openalex.org/W4223534219","https://openalex.org/W4225655543","https://openalex.org/W4247465432","https://openalex.org/W4289835938","https://openalex.org/W4301223505","https://openalex.org/W4319336663","https://openalex.org/W4366550291","https://openalex.org/W6648374539","https://openalex.org/W6683019792","https://openalex.org/W6739073233","https://openalex.org/W6763493577"],"related_works":["https://openalex.org/W4226101702","https://openalex.org/W2110318194","https://openalex.org/W2098836567","https://openalex.org/W3161443230","https://openalex.org/W2619027208","https://openalex.org/W2279539437","https://openalex.org/W2098586728","https://openalex.org/W3166678058","https://openalex.org/W2466416443","https://openalex.org/W2008855908"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,24,94],"investigate":[4],"the":[5,18,30,38,48,55,59,74],"concept":[6],"of":[7,54,58],"regional":[8],"enlarged":[9],"observability":[10],"(ReEnOb)":[11],"for":[12],"fractional":[13],"differential":[14],"equations":[15],"(FDEs)":[16],"with":[17,52],"Hilfer":[19],"derivative.":[20],"To":[21],"proceed":[22],"this,":[23],"develop":[25,87],"an":[26,43],"approach":[27,66],"based":[28],"on":[29,42],"Hilbert":[31],"uniqueness":[32],"method":[33],"(HUM).":[34],"We":[35],"mainly":[36],"reconstruct":[37],"initial":[39,56],"state":[40,76],"\u03bd01":[41],"internal":[44,83],"subregion":[45],"\u03c9":[46],"from":[47],"whole":[49],"domain":[50],"\u03a9":[51],"knowledge":[53],"information":[57],"system":[60],"and":[61,88],"some":[62,81,90],"given":[63],"measurements.":[64],"This":[65],"shows":[67],"that":[68],"it":[69],"is":[70],"possible":[71],"to":[72,98],"obtain":[73],"desired":[75],"between":[77],"two":[78,96],"profiles":[79],"in":[80],"selective":[82],"subregions.":[84],"Our":[85],"findings":[86],"generalize":[89],"known":[91],"results.":[92,102],"Finally,":[93],"give":[95],"examples":[97],"support":[99],"our":[100],"theoretical":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2023-07-02T00:00:00"}