{"id":"https://openalex.org/W4389780499","doi":"https://doi.org/10.3390/axioms12121129","title":"Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays","display_name":"Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays","publication_year":2023,"publication_date":"2023-12-15","ids":{"openalex":"https://openalex.org/W4389780499","doi":"https://doi.org/10.3390/axioms12121129"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12121129","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121129","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/axioms12121129","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102205123","display_name":"Tingting Xie","orcid":"https://orcid.org/0000-0002-4162-4835"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tingting Xie","raw_affiliation_strings":["Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027579610","display_name":"Mengmeng Li","orcid":"https://orcid.org/0000-0001-6926-8716"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengmeng Li","raw_affiliation_strings":["Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"],"raw_orcid":"https://orcid.org/0000-0001-6926-8716","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I178232147"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.5384,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6042304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"12","issue":"12","first_page":"1129","last_page":"1129"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.995199978351593,"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/mathematics","display_name":"Mathematics","score":0.7062549591064453},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5950298309326172},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5691556334495544},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.559486985206604},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.514560878276825},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5045238733291626},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4991023540496826},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4528827965259552},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4463457763195038},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.43496304750442505},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.42753326892852783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16706442832946777}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7062549591064453},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5950298309326172},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5691556334495544},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.559486985206604},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.514560878276825},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5045238733291626},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4991023540496826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4528827965259552},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4463457763195038},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.43496304750442505},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.42753326892852783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16706442832946777},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms12121129","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121129","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:5fba90d767ab49969b05dacb6626e6a9","is_oa":true,"landing_page_url":"https://doaj.org/article/5fba90d767ab49969b05dacb6626e6a9","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 12, p 1129 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12121129","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12121129","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":[{"id":"https://openalex.org/G4997774702","display_name":null,"funder_award_id":"12201148","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5318118642","display_name":null,"funder_award_id":"QKHJC-ZK[2022]YB069","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1511979834","https://openalex.org/W1979238662","https://openalex.org/W1998564383","https://openalex.org/W2000455125","https://openalex.org/W2001952284","https://openalex.org/W2030543960","https://openalex.org/W2160045938","https://openalex.org/W2209066410","https://openalex.org/W2506586217","https://openalex.org/W2558870600","https://openalex.org/W2756709718","https://openalex.org/W2776574981","https://openalex.org/W2793314580","https://openalex.org/W2809148555","https://openalex.org/W2966770440","https://openalex.org/W3085330886","https://openalex.org/W3112649368","https://openalex.org/W4293860355","https://openalex.org/W4301223505","https://openalex.org/W4311791773","https://openalex.org/W4361271538","https://openalex.org/W6747185961","https://openalex.org/W6787603726"],"related_works":["https://openalex.org/W1261320338","https://openalex.org/W2056281781","https://openalex.org/W2942981489","https://openalex.org/W2924035449","https://openalex.org/W2086307616","https://openalex.org/W4243954292","https://openalex.org/W2903509708","https://openalex.org/W2977631248","https://openalex.org/W2753150188","https://openalex.org/W2389579716"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3],"novel":[4],"concept":[5],"of":[6,15,41,48,65],"the":[7,16,28,42,44,63],"impulsive":[8,32,49],"delayed":[9],"Mittag\u2013Leffler-type":[10],"vector":[11],"function,":[12],"an":[13],"extension":[14],"Mittag\u2013Leffler":[17],"matrix":[18],"function.":[19],"It":[20],"is":[21],"essential":[22],"to":[23,30,61],"seek":[24],"explicit":[25,39],"formulas":[26,40],"for":[27],"solutions":[29],"linear":[31],"fractional":[33,50],"differential":[34,51],"delay":[35,52],"equations.":[36],"Based":[37],"on":[38],"solutions,":[43],"finite-time":[45],"stability":[46],"results":[47],"equations":[53],"are":[54],"presented.":[55],"Finally,":[56],"we":[57],"present":[58],"four":[59],"examples":[60],"illustrate":[62],"validity":[64],"our":[66],"theoretical":[67],"results.":[68]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}