{"id":"https://openalex.org/W3154135462","doi":"https://doi.org/10.3390/sym13040650","title":"Symmetry and Its Importance in the Oscillation of Solutions of Differential Equations","display_name":"Symmetry and Its Importance in the Oscillation of Solutions of Differential Equations","publication_year":2021,"publication_date":"2021-04-12","ids":{"openalex":"https://openalex.org/W3154135462","doi":"https://doi.org/10.3390/sym13040650","mag":"3154135462"},"language":"en","primary_location":{"id":"doi:10.3390/sym13040650","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040650","pdf_url":"https://www.mdpi.com/2073-8994/13/4/650/pdf?version=1618208642","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","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/4/650/pdf?version=1618208642","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090377506","display_name":"Ahmed Saeed AlGhamdi","orcid":"https://orcid.org/0000-0002-9165-7600"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmed AlGhamdi","raw_affiliation_strings":["Department of Computer Engineering, College of Computers and Information Technology, Taif University, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-9165-7600","affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, College of Computers and Information Technology, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"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":true,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"],"raw_orcid":null,"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/A5013998288","display_name":"Barakah Almarri","orcid":"https://orcid.org/0000-0002-2878-5300"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Barakah Almarri","raw_affiliation_strings":["Mathematical Science Department, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11564, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-2878-5300","affiliations":[{"raw_affiliation_string":"Mathematical Science Department, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11564, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034511816","display_name":"Omar Bazighifan","orcid":"https://orcid.org/0000-0002-7251-9608"},"institutions":[{"id":"https://openalex.org/I319841309","display_name":"Hadhramout University","ror":"https://ror.org/02kv0px94","country_code":"YE","type":"education","lineage":["https://openalex.org/I319841309"]},{"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","YE"],"is_corresponding":false,"raw_author_name":"Omar Bazighifan","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen","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":"Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen","institution_ids":["https://openalex.org/I319841309"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5080017749"],"corresponding_institution_ids":["https://openalex.org/I4210155399"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.5885,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60632111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"4","first_page":"650","last_page":"650"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9987999796867371,"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":0.7723580002784729},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.7159770131111145},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.6046389937400818},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.586520791053772},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5397030711174011},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.48849761486053467},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4744499623775482},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.4618386924266815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4393472671508789},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38721662759780884},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34344732761383057},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27808865904808044},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0774182379245758},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05580165982246399}],"concepts":[{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.7723580002784729},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.7159770131111145},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.6046389937400818},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.586520791053772},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5397030711174011},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.48849761486053467},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4744499623775482},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.4618386924266815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4393472671508789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38721662759780884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34344732761383057},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27808865904808044},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0774182379245758},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05580165982246399},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/sym13040650","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040650","pdf_url":"https://www.mdpi.com/2073-8994/13/4/650/pdf?version=1618208642","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:19a2e7d005974dfc96f5492aa5b50ef6","is_oa":true,"landing_page_url":"https://doaj.org/article/19a2e7d005974dfc96f5492aa5b50ef6","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 4, p 650 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/4/650/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13040650","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"},{"id":"pmh:oai:zenodo.org:179264","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/179264","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.5281/zenodo.179264","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.179264","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Image"}],"best_oa_location":{"id":"doi:10.3390/sym13040650","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040650","pdf_url":"https://www.mdpi.com/2073-8994/13/4/650/pdf?version=1618208642","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":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"},{"id":"https://openalex.org/F4320337220","display_name":"Deanship of Scientific Research, Princess Nourah Bint Abdulrahman University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3154135462.pdf","grobid_xml":"https://content.openalex.org/works/W3154135462.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1972565057","https://openalex.org/W1995182165","https://openalex.org/W2073949697","https://openalex.org/W2079871064","https://openalex.org/W2402409495","https://openalex.org/W2913406327","https://openalex.org/W2941839657","https://openalex.org/W2942981489","https://openalex.org/W2990891767","https://openalex.org/W3010392372","https://openalex.org/W3015041215","https://openalex.org/W3016080410","https://openalex.org/W3016370273","https://openalex.org/W3016797986","https://openalex.org/W3037447362","https://openalex.org/W3120134854","https://openalex.org/W3126435641","https://openalex.org/W3127581328","https://openalex.org/W3163976345","https://openalex.org/W3165577276"],"related_works":["https://openalex.org/W3210114745","https://openalex.org/W2123585262","https://openalex.org/W2937301577","https://openalex.org/W2062635734","https://openalex.org/W3158420315","https://openalex.org/W3160917256","https://openalex.org/W3176473605","https://openalex.org/W2367945514","https://openalex.org/W2356614427","https://openalex.org/W2072100489"],"abstract_inverted_index":{"Oscillation":[0],"and":[1,15,63],"symmetry":[2],"play":[3],"an":[4],"important":[5],"role":[6],"in":[7,17,67,74],"many":[8],"applications":[9],"such":[10],"as":[11],"engineering,":[12],"physics,":[13],"medicine,":[14],"vibration":[16],"flight.":[18],"The":[19],"purpose":[20],"of":[21,29],"this":[22],"article":[23],"is":[24],"to":[25,50,76],"explore":[26],"the":[27,52,68,78],"oscillation":[28],"fourth-order":[30],"differential":[31],"equations":[32],"with":[33],"delay":[34],"arguments.":[35],"New":[36],"Kamenev-type":[37],"oscillatory":[38],"properties":[39],"are":[40,43,72],"established,":[41],"which":[42],"based":[44],"on":[45],"a":[46,56],"suitable":[47],"Riccati":[48],"method":[49],"reduce":[51],"main":[53,79],"equation":[54],"into":[55],"first-order":[57],"inequality.":[58],"Our":[59],"new":[60],"results":[61,66],"extend":[62],"simplify":[64],"existing":[65],"previous":[69],"studies.":[70],"Examples":[71],"presented":[73],"order":[75],"clarify":[77],"results.":[80]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}