{"id":"https://openalex.org/W4220872035","doi":"https://doi.org/10.3390/axioms11020052","title":"Neutral Differential Equations of Fourth-Order: New Asymptotic Properties of Solutions","display_name":"Neutral Differential Equations of Fourth-Order: New Asymptotic Properties of Solutions","publication_year":2022,"publication_date":"2022-01-28","ids":{"openalex":"https://openalex.org/W4220872035","doi":"https://doi.org/10.3390/axioms11020052"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11020052","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020052","pdf_url":"https://www.mdpi.com/2075-1680/11/2/52/pdf?version=1645699994","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/2075-1680/11/2/52/pdf?version=1645699994","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039924294","display_name":"Ali Muhib","orcid":"https://orcid.org/0000-0003-3844-7820"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]},{"id":"https://openalex.org/I78137547","display_name":"Ibb University","ror":"https://ror.org/00fhcxc56","country_code":"YE","type":"education","lineage":["https://openalex.org/I78137547"]}],"countries":["EG","YE"],"is_corresponding":false,"raw_author_name":"Ali Muhib","raw_affiliation_strings":["Department of Mathematics, Faculty of Education\u2014Al-Nadirah, Ibb University, Ibb 70270, Yemen","Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education\u2014Al-Nadirah, Ibb University, Ibb 70270, Yemen","institution_ids":["https://openalex.org/I78137547"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074973583","display_name":"Osama Moaaz","orcid":"https://orcid.org/0000-0003-3850-1022"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["EG","IT"],"is_corresponding":true,"raw_author_name":"Osama Moaaz","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080017749","display_name":"Clemente Cesarano","orcid":"https://orcid.org/0000-0002-1694-7907"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088545047","display_name":"Sameh Askar","orcid":"https://orcid.org/0000-0002-1167-2430"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Sameh Askar","raw_affiliation_strings":["Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085382303","display_name":"Elmetwally M. Elabbasy","orcid":"https://orcid.org/0000-0002-9864-3615"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Elmetwally M. Elabbasy","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5074973583"],"corresponding_institution_ids":["https://openalex.org/I159247623","https://openalex.org/I4210155399"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.2023,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91544118,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"11","issue":"2","first_page":"52","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9991000294685364,"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/oscillation","display_name":"Oscillation (cell signaling)","score":0.8393637537956238},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.6246759295463562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.535434365272522},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5231450796127319},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5045629739761353},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47886011004447937},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4280078411102295},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.41617876291275024},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24995216727256775},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0919812023639679},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06825590133666992}],"concepts":[{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.8393637537956238},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.6246759295463562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.535434365272522},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5231450796127319},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5045629739761353},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47886011004447937},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4280078411102295},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.41617876291275024},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24995216727256775},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0919812023639679},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06825590133666992},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11020052","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020052","pdf_url":"https://www.mdpi.com/2075-1680/11/2/52/pdf?version=1645699994","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:0b08f12331634c639cf4ee9f49d77b6b","is_oa":true,"landing_page_url":"https://doaj.org/article/0b08f12331634c639cf4ee9f49d77b6b","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 2, p 52 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/2/52/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11020052","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 11; Issue 2; Pages: 52","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11020052","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020052","pdf_url":"https://www.mdpi.com/2075-1680/11/2/52/pdf?version=1645699994","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/G3855766620","display_name":null,"funder_award_id":"Saudi Arabia.","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"},{"id":"https://openalex.org/G7705553812","display_name":null,"funder_award_id":"Project number (RSP-2022/167)","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"},{"id":"https://openalex.org/G8239988234","display_name":null,"funder_award_id":"Riyadh","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"},{"id":"https://openalex.org/G8274354555","display_name":null,"funder_award_id":"RSP-2022/167","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220872035.pdf","grobid_xml":"https://content.openalex.org/works/W4220872035.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W106332986","https://openalex.org/W568096069","https://openalex.org/W1549746015","https://openalex.org/W1981480416","https://openalex.org/W1994975281","https://openalex.org/W2006505167","https://openalex.org/W2019602482","https://openalex.org/W2020155377","https://openalex.org/W2026701610","https://openalex.org/W2042664903","https://openalex.org/W2081962399","https://openalex.org/W2113754706","https://openalex.org/W2120201283","https://openalex.org/W2966927609","https://openalex.org/W2999252454","https://openalex.org/W3012038344","https://openalex.org/W3040078714","https://openalex.org/W3088263709","https://openalex.org/W3162354609","https://openalex.org/W3195512502","https://openalex.org/W3197120291","https://openalex.org/W3198857388","https://openalex.org/W6766586468","https://openalex.org/W6774761888"],"related_works":["https://openalex.org/W2004735650","https://openalex.org/W1551019254","https://openalex.org/W3158420315","https://openalex.org/W3160917256","https://openalex.org/W2356614427","https://openalex.org/W2072100489","https://openalex.org/W2076457760","https://openalex.org/W2294866254","https://openalex.org/W2950671338","https://openalex.org/W2596503610"],"abstract_inverted_index":{"In":[0,49],"this":[1],"work,":[2],"we":[3,53],"will":[4,54],"derive":[5],"new":[6,60],"asymptotic":[7],"properties":[8,57],"of":[9,13,35,51,65,68,80],"the":[10,14,20,63,66,69,78,81],"positive":[11],"solutions":[12,67],"fourth-order":[15],"neutral":[16],"differential":[17],"equation":[18],"with":[19],"non-canonical":[21],"factor.":[22],"We":[23],"follow":[24],"an":[25,36],"improved":[26],"approach":[27],"that":[28,39],"enables":[29],"us":[30],"to":[31,46,58,76],"create":[32],"oscillation":[33,64],"criteria":[34,61],"iterative":[37],"nature":[38],"can":[40],"be":[41],"applied":[42],"more":[43],"than":[44],"once":[45],"test":[47],"oscillation.":[48],"light":[50],"this,":[52],"use":[55],"these":[56],"obtain":[59],"for":[62],"studied":[70],"equation.":[71],"An":[72],"example":[73],"is":[74],"given":[75],"show":[77],"applicability":[79],"main":[82],"results.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
