{"id":"https://openalex.org/W3207524541","doi":"https://doi.org/10.3390/sym13101895","title":"Analysis on \u03c8-Hilfer Fractional Impulsive Differential Equations","display_name":"Analysis on \u03c8-Hilfer Fractional Impulsive Differential Equations","publication_year":2021,"publication_date":"2021-10-08","ids":{"openalex":"https://openalex.org/W3207524541","doi":"https://doi.org/10.3390/sym13101895","mag":"3207524541"},"language":"en","primary_location":{"id":"doi:10.3390/sym13101895","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101895","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1895/pdf?version=1634112611","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/10/1895/pdf?version=1634112611","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101895079","display_name":"K. Karthikeyan","orcid":"https://orcid.org/0000-0002-4138-7067"},"institutions":[{"id":"https://openalex.org/I4210133257","display_name":"KPR Institute of Engineering and Technology","ror":"https://ror.org/02q9f3a53","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210133257"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kulandhaivel Karthikeyan","raw_affiliation_strings":["Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641 407, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0002-4138-7067","affiliations":[{"raw_affiliation_string":"Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641 407, Tamil Nadu, India","institution_ids":["https://openalex.org/I4210133257"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044068151","display_name":"P. Karthikeyan","orcid":"https://orcid.org/0000-0001-6712-9819"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panjaiyan Karthikeyan","raw_affiliation_strings":["Department of Mathematics, Sri Vasavi College, Erode 638 316, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0001-6712-9819","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Vasavi College, Erode 638 316, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070501286","display_name":"Dimplekumar Chalishajar","orcid":"https://orcid.org/0000-0002-6146-5544"},"institutions":[{"id":"https://openalex.org/I185641255","display_name":"Virginia Military Institute","ror":"https://ror.org/01ngnm118","country_code":"US","type":"education","lineage":["https://openalex.org/I185641255"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dimplekumar N. Chalishajar","raw_affiliation_strings":["Department of Applied Mathematics, Virginia Military Institute, 435 Mallory Hall, Lexington, VA 24450, USA"],"raw_orcid":"https://orcid.org/0000-0002-6146-5544","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Virginia Military Institute, 435 Mallory Hall, Lexington, VA 24450, USA","institution_ids":["https://openalex.org/I185641255"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Duraisamy Senthil Raja","orcid":"https://orcid.org/0000-0001-7129-8180"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Duraisamy Senthil Raja","raw_affiliation_strings":["Department of Mathematics, K.S.Rangasamy College of Technology, Tiruchengode 637 215, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0001-7129-8180","affiliations":[{"raw_affiliation_string":"Department of Mathematics, K.S.Rangasamy College of Technology, Tiruchengode 637 215, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080027135","display_name":"Ponnusamy Sundararajan","orcid":"https://orcid.org/0000-0002-4227-9519"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ponnusamy Sundararajan","raw_affiliation_strings":["Department of Mathematics, Arinagar Anna Government Arts College, Namakkal 637 002, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0002-4227-9519","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Arinagar Anna Government Arts College, Namakkal 637 002, Tamil Nadu, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5070501286"],"corresponding_institution_ids":["https://openalex.org/I185641255"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.9615,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.94711198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"10","first_page":"1895","last_page":"1895"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9998999834060669,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/fractional-calculus","display_name":"Fractional calculus","score":0.7002270221710205},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6923925876617432},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.6620374917984009},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6426845788955688},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5714938640594482},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4577542543411255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44904932379722595},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.44418802857398987},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44416069984436035},{"id":"https://openalex.org/keywords/analytic-semigroup","display_name":"Analytic semigroup","score":0.42545393109321594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38446474075317383}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7002270221710205},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6923925876617432},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.6620374917984009},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6426845788955688},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5714938640594482},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4577542543411255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44904932379722595},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.44418802857398987},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44416069984436035},{"id":"https://openalex.org/C2779751289","wikidata":"https://www.wikidata.org/wiki/Q485292","display_name":"Analytic semigroup","level":3,"score":0.42545393109321594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38446474075317383},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13101895","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101895","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1895/pdf?version=1634112611","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0685079dc92947d69733254ad01de207","is_oa":true,"landing_page_url":"https://doaj.org/article/0685079dc92947d69733254ad01de207","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":"Symmetry, Vol 13, Iss 10, p 1895 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/10/1895/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13101895","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13101895","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101895","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1895/pdf?version=1634112611","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3207524541.pdf","grobid_xml":"https://content.openalex.org/works/W3207524541.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W433794350","https://openalex.org/W604143053","https://openalex.org/W1527296550","https://openalex.org/W1971828127","https://openalex.org/W1991397548","https://openalex.org/W2395672747","https://openalex.org/W2808745722","https://openalex.org/W2810489467","https://openalex.org/W2885040951","https://openalex.org/W2963670184","https://openalex.org/W3027423968","https://openalex.org/W3043443187","https://openalex.org/W3121967304","https://openalex.org/W3215547433","https://openalex.org/W6648374539"],"related_works":["https://openalex.org/W1964813471","https://openalex.org/W2975981742","https://openalex.org/W2364132950","https://openalex.org/W2915024987","https://openalex.org/W1964251668","https://openalex.org/W4288598325","https://openalex.org/W2945496170","https://openalex.org/W1805067046","https://openalex.org/W2560261823","https://openalex.org/W4386000381"],"abstract_inverted_index":{"In":[0],"this":[1],"manuscript,":[2],"we":[3],"establish":[4],"the":[5,31,42,65,73,86,96,103,116],"existence":[6],"of":[7,9,45,64,75,77,95],"results":[8,66],"fractional":[10,16],"impulsive":[11],"differential":[12],"equations":[13],"involving":[14],"\u03c8-Hilfer":[15],"derivative":[17],"and":[18,36,56,59,89],"almost":[19],"sectorial":[20,87],"operators":[21],"using":[22],"Schauder":[23],"fixed-point":[24],"theorem.":[25],"We":[26,39,48],"discuss":[27],"two":[28],"cases,":[29],"if":[30],"associated":[32],"semigroup":[33],"is":[34,112],"compact":[35],"noncompact,":[37],"respectively.":[38],"consider":[40],"here":[41],"higher-dimensional":[43],"system":[44],"integral":[46],"equations.":[47],"present":[49],"herewith":[50],"new":[51,57],"theoretical":[52],"results,":[53],"structural":[54],"investigations,":[55],"models":[58],"approaches.":[60],"Some":[61],"special":[62],"cases":[63],"are":[67],"discussed":[68],"as":[69,106],"well.":[70,107],"Due":[71],"to":[72,102,114],"nature":[74],"measurement":[76],"noncompactness":[78],"theory,":[79],"there":[80],"exists":[81],"a":[82,109],"strong":[83],"relationship":[84],"between":[85],"operator":[88],"symmetry.":[90],"When":[91],"working":[92],"on":[93],"either":[94],"concepts,":[97],"it":[98],"can":[99],"be":[100],"applied":[101],"other":[104],"one":[105],"Finally,":[108],"case":[110],"study":[111],"presented":[113],"demonstrate":[115],"major":[117],"theory.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2021-10-25T00:00:00"}
