{"id":"https://openalex.org/W4416665292","doi":"https://doi.org/10.3390/axioms14120859","title":"Fractional Powers of Anti-Triangular Operator Matrices and Their Applications","display_name":"Fractional Powers of Anti-Triangular Operator Matrices and Their Applications","publication_year":2025,"publication_date":"2025-11-24","ids":{"openalex":"https://openalex.org/W4416665292","doi":"https://doi.org/10.3390/axioms14120859"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14120859","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14120859","pdf_url":null,"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://doi.org/10.3390/axioms14120859","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lei Zhao","orcid":"https://orcid.org/0009-0005-4215-8353"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"],"raw_orcid":"https://orcid.org/0009-0005-4215-8353","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","institution_ids":["https://openalex.org/I2722730"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101642001","display_name":"Yongqing Fu","orcid":"https://orcid.org/0000-0003-2124-3039"},"institutions":[{"id":"https://openalex.org/I4210155205","display_name":"Marine Institute","ror":"https://ror.org/05581wm82","country_code":"IE","type":"funder","lineage":["https://openalex.org/I4210155205"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Yongqing Fu","raw_affiliation_strings":["School of Methematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Methematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China","institution_ids":["https://openalex.org/I4210155205"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081987954","display_name":"Junjie Huang","orcid":"https://orcid.org/0000-0003-2382-4443"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junjie Huang","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China","institution_ids":["https://openalex.org/I2722730"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081987954"],"corresponding_institution_ids":["https://openalex.org/I2722730"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.34765056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"12","first_page":"859","last_page":"859"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.22370000183582306,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.22370000183582306,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.13729999959468842,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.11410000175237656,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/operator","display_name":"Operator (biology)","score":0.652400016784668},{"id":"https://openalex.org/keywords/operator-matrix","display_name":"Operator matrix","score":0.5654000043869019},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.517799973487854},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5170000195503235},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5029000043869019},{"id":"https://openalex.org/keywords/matrix-representation","display_name":"Matrix representation","score":0.4876999855041504},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4819999933242798},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4307999908924103}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7394000291824341},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.652400016784668},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.5654000043869019},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.517799973487854},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5170000195503235},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5029000043869019},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.4876999855041504},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.41290000081062317},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.4115000069141388},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.4050000011920929},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39100000262260437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38850000500679016},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3522000014781952},{"id":"https://openalex.org/C15460668","wikidata":"https://www.wikidata.org/wiki/Q1644451","display_name":"Pseudo-differential operator","level":5,"score":0.31060001254081726},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2678999900817871},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14120859","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14120859","pdf_url":null,"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:79383bdc264c46eb96cb5c3416fc87f0","is_oa":true,"landing_page_url":"https://doaj.org/article/79383bdc264c46eb96cb5c3416fc87f0","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 14, Iss 12, p 859 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14120859","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14120859","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W35304917","https://openalex.org/W1990878990","https://openalex.org/W2007531938","https://openalex.org/W2011216114","https://openalex.org/W2018872110","https://openalex.org/W2027392793","https://openalex.org/W2045844899","https://openalex.org/W2076687762","https://openalex.org/W2093169427","https://openalex.org/W2529729591","https://openalex.org/W2575384730","https://openalex.org/W2783338625","https://openalex.org/W3014410229","https://openalex.org/W3016303664","https://openalex.org/W3196360220","https://openalex.org/W4322615330","https://openalex.org/W4399756434","https://openalex.org/W4407984304"],"related_works":[],"abstract_inverted_index":{"The":[0],"concept":[1],"of":[2,5,13,26,55,68,71,86,95,113],"fractional":[3,69,84,111],"powers":[4,70,85,112],"operators":[6],"was":[7],"initially":[8],"developed":[9],"within":[10],"the":[11,24,37,52,65,83,92,102,110,114,120],"framework":[12],"functional":[14],"analysis":[15],"and":[16,32,46],"has":[17,41],"since":[18],"played":[19],"a":[20,44,107],"significant":[21],"role":[22],"in":[23],"study":[25],"evolution":[27],"equations,":[28,31],"abstract":[29],"differential":[30,128],"complex":[33],"dynamical":[34],"systems.":[35],"Meanwhile,":[36],"operator":[38,73,88,97],"matrix":[39],"approach":[40],"emerged":[42],"as":[43],"powerful":[45],"widely":[47],"used":[48],"tool":[49],"for":[50,82,109],"analyzing":[51],"structural":[53],"properties":[54],"operators.":[56],"Motivated":[57],"by":[58,90],"these":[59],"developments,":[60],"this":[61],"paper":[62],"focuses":[63],"on":[64,101],"explicit":[66,80],"computation":[67],"anti-triangular":[72,116],"matrices.":[74,98],"Specifically,":[75],"we":[76,105],"first":[77],"derive":[78],"an":[79],"formula":[81],"off-diagonal":[87],"matrices":[89],"employing":[91],"formal":[93],"determinant":[94],"block":[96],"Then,":[99],"based":[100],"Schur":[103],"factorization,":[104],"obtain":[106],"representation":[108],"general":[115],"case.":[117],"As":[118],"applications,":[119],"obtained":[121],"results":[122],"are":[123],"further":[124],"applied":[125],"to":[126],"certain":[127],"equations.":[129]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-11-25T00:00:00"}