{"id":"https://openalex.org/W3208364502","doi":"https://doi.org/10.3390/sym13112015","title":"Delay Differential Equations of Fourth-Order: Oscillation and Asymptotic Properties of Solutions","display_name":"Delay Differential Equations of Fourth-Order: Oscillation and Asymptotic Properties of Solutions","publication_year":2021,"publication_date":"2021-10-24","ids":{"openalex":"https://openalex.org/W3208364502","doi":"https://doi.org/10.3390/sym13112015","mag":"3208364502"},"language":"en","primary_location":{"id":"doi:10.3390/sym13112015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112015","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2015/pdf?version=1635846604","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/2073-8994/13/11/2015/pdf?version=1635846604","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034511816","display_name":"Omar Bazighifan","orcid":"https://orcid.org/0000-0002-7251-9608"},"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":true,"raw_author_name":"Omar Bazighifan","raw_affiliation_strings":["Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7251-9608","affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077561048","display_name":"Maryam Al-Kandari","orcid":"https://orcid.org/0000-0002-1117-5653"},"institutions":[{"id":"https://openalex.org/I36721946","display_name":"Kuwait University","ror":"https://ror.org/021e5j056","country_code":"KW","type":"education","lineage":["https://openalex.org/I36721946"]}],"countries":["KW"],"is_corresponding":false,"raw_author_name":"Maryam Al-Kandari","raw_affiliation_strings":["Department of Mathematics, Kuwait University, P.O. Box 5969, Safat, Khaldiyah City 13060, Kuwait"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kuwait University, P.O. Box 5969, Safat, Khaldiyah City 13060, Kuwait","institution_ids":["https://openalex.org/I36721946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062467405","display_name":"Khalil S. Al-Ghafri","orcid":"https://orcid.org/0000-0002-4392-0742"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khalil S. Al-Ghafri","raw_affiliation_strings":["University of Technology and Applied Sciences, P.O. Box 14, Ibri 516, Oman"],"raw_orcid":"https://orcid.org/0000-0002-4392-0742","affiliations":[{"raw_affiliation_string":"University of Technology and Applied Sciences, P.O. Box 14, Ibri 516, Oman","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011299544","display_name":"F. Ghanim","orcid":"https://orcid.org/0000-0001-8586-2539"},"institutions":[{"id":"https://openalex.org/I29891158","display_name":"University of Sharjah","ror":"https://ror.org/00engpz63","country_code":"AE","type":"education","lineage":["https://openalex.org/I29891158"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"F. Ghanim","raw_affiliation_strings":["Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates"],"raw_orcid":"https://orcid.org/0000-0001-8586-2539","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates","institution_ids":["https://openalex.org/I29891158"]}]},{"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"],"raw_orcid":"https://orcid.org/0000-0002-1167-2430","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/A5020913149","display_name":"Georgia Irina Oros","orcid":"https://orcid.org/0000-0003-2902-4455"},"institutions":[{"id":"https://openalex.org/I162871001","display_name":"University of Oradea","ror":"https://ror.org/00wzhv093","country_code":"RO","type":"education","lineage":["https://openalex.org/I162871001"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Georgia Irina Oros","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania"],"raw_orcid":"https://orcid.org/0000-0003-2902-4455","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania","institution_ids":["https://openalex.org/I162871001"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5020913149","https://openalex.org/A5034511816"],"corresponding_institution_ids":["https://openalex.org/I162871001","https://openalex.org/I4210155399"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9374,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73162011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"11","first_page":"2015","last_page":"2015"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9997000098228455,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991999864578247,"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/oscillation","display_name":"Oscillation (cell signaling)","score":0.6933490633964539},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.664529025554657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6118015050888062},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.6030895113945007},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.5421957969665527},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5355017185211182},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.531846284866333},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4806065261363983},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47261619567871094},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4567684829235077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45342350006103516},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.43783971667289734},{"id":"https://openalex.org/keywords/method-of-matched-asymptotic-expansions","display_name":"Method of matched asymptotic expansions","score":0.4323868453502655},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.41921788454055786},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13710877299308777}],"concepts":[{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.6933490633964539},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.664529025554657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6118015050888062},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.6030895113945007},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.5421957969665527},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5355017185211182},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.531846284866333},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4806065261363983},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47261619567871094},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4567684829235077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45342350006103516},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.43783971667289734},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.4323868453502655},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.41921788454055786},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13710877299308777},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"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":3,"locations":[{"id":"doi:10.3390/sym13112015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112015","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2015/pdf?version=1635846604","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:0ae3c2db0ce7482ca852b363ad16d63a","is_oa":true,"landing_page_url":"https://doaj.org/article/0ae3c2db0ce7482ca852b363ad16d63a","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 11, p 2015 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/2015/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13112015","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/sym13112015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112015","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2015/pdf?version=1635846604","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3208364502.pdf","grobid_xml":"https://content.openalex.org/works/W3208364502.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W572159918","https://openalex.org/W1549746015","https://openalex.org/W1988504596","https://openalex.org/W1994975281","https://openalex.org/W1995182165","https://openalex.org/W2006505167","https://openalex.org/W2019602482","https://openalex.org/W2024472156","https://openalex.org/W2042664903","https://openalex.org/W2057343462","https://openalex.org/W2061983062","https://openalex.org/W2079871064","https://openalex.org/W2120201283","https://openalex.org/W2188565877","https://openalex.org/W2295381585","https://openalex.org/W2530624344","https://openalex.org/W2590628450","https://openalex.org/W2755293947","https://openalex.org/W2799290197","https://openalex.org/W2902273760","https://openalex.org/W2971355763","https://openalex.org/W2995153360","https://openalex.org/W3004422340","https://openalex.org/W3004911550","https://openalex.org/W3012038344","https://openalex.org/W3037447362","https://openalex.org/W3046212638","https://openalex.org/W3121918627","https://openalex.org/W3161793875","https://openalex.org/W3201654168","https://openalex.org/W3204570872","https://openalex.org/W3207079867","https://openalex.org/W6647384621","https://openalex.org/W6687327942","https://openalex.org/W6774761888","https://openalex.org/W6779785757"],"related_works":["https://openalex.org/W2357141384","https://openalex.org/W2390991069","https://openalex.org/W2348576774","https://openalex.org/W2362061707","https://openalex.org/W2150987529","https://openalex.org/W2352047463","https://openalex.org/W2070142800","https://openalex.org/W2386228494","https://openalex.org/W2073949697","https://openalex.org/W2050866979"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"by":[3],"using":[4],"the":[5,33,41,51],"comparison":[6],"method":[7],"and":[8],"Riccati":[9],"transformation,":[10],"we":[11],"obtain":[12],"some":[13],"oscillation":[14],"criteria":[15,28],"of":[16,18,22],"solutions":[17,55],"delay":[19],"differential":[20,57],"equations":[21],"fourth-order":[23],"in":[24,32,49],"canonical":[25],"form.":[26],"These":[27],"complement":[29],"those":[30],"results":[31],"literature.":[34],"We":[35],"give":[36],"two":[37],"examples":[38],"to":[39,56],"illustrate":[40],"main":[42],"results.":[43],"Symmetry":[44],"plays":[45],"an":[46],"essential":[47],"role":[48],"determining":[50],"correct":[52],"methods":[53],"for":[54],"equations.":[58]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
