{"id":"https://openalex.org/W4308332761","doi":"https://doi.org/10.3390/axioms11110611","title":"Existence Solutions for Implicit Fractional Relaxation Differential Equations with Impulsive Delay Boundary Conditions","display_name":"Existence Solutions for Implicit Fractional Relaxation Differential Equations with Impulsive Delay Boundary Conditions","publication_year":2022,"publication_date":"2022-11-02","ids":{"openalex":"https://openalex.org/W4308332761","doi":"https://doi.org/10.3390/axioms11110611"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11110611","doi":"https://doi.org/10.3390/axioms11110611","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110611","pdf_url":"https://www.mdpi.com/2075-1680/11/11/611/pdf?version=1667370487","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,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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"},"parent_works":[],"lineage":["https://openalex.org/W4308332761"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/11/611/pdf?version=1667370487","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071140390","display_name":"Varaporn Wattanakejorn","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210097440","display_name":"Suan Dusit University","ror":"https://ror.org/00x7vzk16","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210097440"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Varaporn Wattanakejorn","raw_affiliation_strings":["Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand","institution_ids":["https://openalex.org/I4210097440"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044068151","display_name":"Panjaiyan Karthikeyan","orcid":"https://orcid.org/0000-0001-6712-9819","observed_orcids":["https://orcid.org/0000-0001-6712-9819"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panjaiyan Karthikeyann","raw_affiliation_strings":["Department of Mathematics, Sri Vasavi College, Erode 638316, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Vasavi College, Erode 638316, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075427039","display_name":"Sadhasivam Poornima","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sadhasivam Poornima","raw_affiliation_strings":["Department of Mathematics, Sri Vasavi College, Erode 638316, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Vasavi College, Erode 638316, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101895079","display_name":"K. Karthikeyan","orcid":"https://orcid.org/0000-0002-4138-7067","observed_orcids":["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":true,"raw_author_name":"Kulandhaivel Karthikeyan","raw_affiliation_strings":["Department of Mathematics & Centre for Research and Development, KPR Institute of Engineering and Technology, Coimbatore 641407, India"],"raw_orcid":"https://orcid.org/0000-0002-4138-7067","affiliations":[{"raw_affiliation_string":"Department of Mathematics & Centre for Research and Development, KPR Institute of Engineering and Technology, Coimbatore 641407, India","institution_ids":["https://openalex.org/I4210133257"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065323596","display_name":"Thanin Sitthiwirattham","orcid":"https://orcid.org/0000-0002-8455-1402","observed_orcids":["https://orcid.org/0000-0002-8455-1402"]},"institutions":[{"id":"https://openalex.org/I4210097440","display_name":"Suan Dusit University","ror":"https://ror.org/00x7vzk16","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210097440"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Thanin Sitthiwirattham","raw_affiliation_strings":["Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-8455-1402","affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand","institution_ids":["https://openalex.org/I4210097440"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065323596","https://openalex.org/A5101895079"],"corresponding_institution_ids":["https://openalex.org/I4210097440","https://openalex.org/I4210133257"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1675},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1675},"fwci":2.244,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8721153,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"11","issue":"11","first_page":"611","last_page":"611"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/impulsive-differential-equations","display_name":"impulsive differential equations","score":0.8479999899864197},{"id":"https://openalex.org/keywords/delay-differential-equations","display_name":"delay differential equations","score":0.8330000042915344},{"id":"https://openalex.org/keywords/implicit-differential-equations","display_name":"implicit differential equations","score":0.8600000143051147},{"id":"https://openalex.org/keywords/boundary-value-problems","display_name":"boundary value problems","score":0.8849999904632568},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.9120000004768372},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.9919999837875366},{"id":"https://openalex.org/keywords/nonlinear-fractional-differential-equations","display_name":"nonlinear fractional differential equations","score":0.6919999718666077}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.747157871723175},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.734011709690094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.702139675617218},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.6838662028312683},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.6066072583198547},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6059873700141907},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5893222093582153},{"id":"https://openalex.org/C2775958659","wikidata":"https://www.wikidata.org/wiki/Q5165690","display_name":"Contraction principle","level":3,"score":0.5624339580535889},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5562686920166016},{"id":"https://openalex.org/C28642324","wikidata":"https://www.wikidata.org/wiki/Q656176","display_name":"Schauder fixed point theorem","level":4,"score":0.5217815041542053},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5157606601715088},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4354471266269684},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4226859211921692},{"id":"https://openalex.org/C2780549194","wikidata":"https://www.wikidata.org/wiki/Q220680","display_name":"Banach fixed-point theorem","level":3,"score":0.41596999764442444},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33827710151672363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09492763876914978},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms11110611","doi":"https://doi.org/10.3390/axioms11110611","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110611","pdf_url":"https://www.mdpi.com/2075-1680/11/11/611/pdf?version=1667370487","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,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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:05d70bececbe400681679c06558a0310","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/05d70bececbe400681679c06558a0310","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,"listed_in":[],"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 11, Iss 11, p 611 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms11110611","doi":"https://doi.org/10.3390/axioms11110611","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110611","pdf_url":"https://www.mdpi.com/2075-1680/11/11/611/pdf?version=1667370487","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,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320318713","display_name":"Suan Dusit University","ror":"https://ror.org/00x7vzk16"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4308332761.pdf","grobid_xml":"https://content.openalex.org/works/W4308332761.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W2305413368","https://openalex.org/W2464975856","https://openalex.org/W2570396616","https://openalex.org/W2905375821","https://openalex.org/W2962930540","https://openalex.org/W2967296812","https://openalex.org/W2969132498","https://openalex.org/W3006312278","https://openalex.org/W3035701830","https://openalex.org/W3045096239","https://openalex.org/W3119835114","https://openalex.org/W3150876583","https://openalex.org/W3209705542","https://openalex.org/W4211119976","https://openalex.org/W4220671680","https://openalex.org/W4220742275","https://openalex.org/W4312540940","https://openalex.org/W6748396876"],"related_works":["https://openalex.org/W4393327039","https://openalex.org/W4393169618","https://openalex.org/W4404046312","https://openalex.org/W4312540940","https://openalex.org/W3119740011","https://openalex.org/W2467759214","https://openalex.org/W4389914151","https://openalex.org/W2370658410","https://openalex.org/W3033289399","https://openalex.org/W2988895020"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,12],"this":[3],"paper":[4],"is":[5,44],"to":[6],"study":[7],"the":[8,32,38,48],"existence":[9],"and":[10,37],"uniqueness":[11],"solutions":[13],"for":[14],"nonlinear":[15],"fractional":[16],"relaxation":[17],"impulsive":[18],"implicit":[19],"delay":[20],"differential":[21],"equations":[22],"with":[23],"boundary":[24],"conditions.":[25],"Some":[26],"findings":[27],"are":[28],"established":[29],"by":[30],"applying":[31],"Banach":[33],"contraction":[34],"mapping":[35],"principle":[36],"Schauder":[39],"fixed-point":[40],"theorem.":[41],"An":[42],"example":[43],"provided":[45],"that":[46],"illustrates":[47],"theoretical":[49],"results.":[50]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2022-11-11T00:00:00"}