{"id":"https://openalex.org/W4400295904","doi":"https://doi.org/10.3390/sym16070817","title":"New Monotonic Properties for Solutions of Odd-Order Advanced Nonlinear Differential Equations","display_name":"New Monotonic Properties for Solutions of Odd-Order Advanced Nonlinear Differential Equations","publication_year":2024,"publication_date":"2024-06-29","ids":{"openalex":"https://openalex.org/W4400295904","doi":"https://doi.org/10.3390/sym16070817"},"language":"en","primary_location":{"id":"doi:10.3390/sym16070817","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070817","pdf_url":"https://www.mdpi.com/2073-8994/16/7/817/pdf?version=1720680844","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/2073-8994/16/7/817/pdf?version=1720680844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046235767","display_name":"Asma Al-Jaser","orcid":"https://orcid.org/0009-0006-7219-8193"},"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":"Asma Al-Jaser","raw_affiliation_strings":["Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019347203","display_name":"Belgees Qaraad","orcid":"https://orcid.org/0000-0002-2115-0791"},"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":true,"raw_author_name":"Belgees Qaraad","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"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102926378","display_name":"F. M. Alharbi","orcid":"https://orcid.org/0000-0001-6265-9925"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Faizah Alharbi","raw_affiliation_strings":["Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 24227, Saudi Arabia","Mathematics Department, Faculty of Sciences, Umm Al-Quraa University, Makkah 24227, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 24227, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]},{"raw_affiliation_string":"Mathematics Department, Faculty of Sciences, Umm Al-Quraa University, Makkah 24227, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053268193","display_name":"Stefano Serra\u2010Capizzano","orcid":"https://orcid.org/0000-0001-9477-109X"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]},{"id":"https://openalex.org/I115752224","display_name":"University of Insubria","ror":"https://ror.org/00s409261","country_code":"IT","type":"education","lineage":["https://openalex.org/I115752224"]}],"countries":["IT","SE"],"is_corresponding":false,"raw_author_name":"Stefano Serra-Capizzano","raw_affiliation_strings":["Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy","Division of Scientific Computing, Department of Information Technology, Uppsala University, L\u00e4gerhyddsv 2, Hus 2, P.O. Box 337, SE-751 05 Uppsala, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy","institution_ids":["https://openalex.org/I115752224"]},{"raw_affiliation_string":"Division of Scientific Computing, Department of Information Technology, Uppsala University, L\u00e4gerhyddsv 2, Hus 2, P.O. Box 337, SE-751 05 Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019347203"],"corresponding_institution_ids":["https://openalex.org/I159247623"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9912,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.71470697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"7","first_page":"817","last_page":"817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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":0.9994000196456909,"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/monotonic-function","display_name":"Monotonic function","score":0.8703298568725586},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.617681086063385},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.616581916809082},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6003307104110718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5991249084472656},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.5835301876068115},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5433966517448425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5433370471000671},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5378315448760986},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.45403361320495605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37940514087677},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1400129199028015}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8703298568725586},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.617681086063385},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.616581916809082},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6003307104110718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5991249084472656},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.5835301876068115},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5433966517448425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5433370471000671},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5378315448760986},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.45403361320495605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37940514087677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1400129199028015},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym16070817","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070817","pdf_url":"https://www.mdpi.com/2073-8994/16/7/817/pdf?version=1720680844","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:DiVA.org:uu-543676","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-543676","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:3c9f364edcd741758e2d4553f25f2aec","is_oa":true,"landing_page_url":"https://doaj.org/article/3c9f364edcd741758e2d4553f25f2aec","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":"Symmetry, Vol 16, Iss 7, p 817 (2024)","raw_type":"article"},{"id":"pmh:oai:irinsubria.uninsubria.it:11383/2186673","is_oa":true,"landing_page_url":"https://hdl.handle.net/11383/2186673","pdf_url":null,"source":{"id":"https://openalex.org/S4377196351","display_name":"IrInSubria (University of Insubria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115752224","host_organization_name":"University of Insubria","host_organization_lineage":["https://openalex.org/I115752224"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/sym16070817","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16070817","pdf_url":"https://www.mdpi.com/2073-8994/16/7/817/pdf?version=1720680844","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":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400295904.pdf"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W24304565","https://openalex.org/W67884324","https://openalex.org/W106332986","https://openalex.org/W572159918","https://openalex.org/W1432937839","https://openalex.org/W1964053806","https://openalex.org/W1994975281","https://openalex.org/W2004604977","https://openalex.org/W2006505167","https://openalex.org/W2008817996","https://openalex.org/W2020155377","https://openalex.org/W2073949697","https://openalex.org/W2076682495","https://openalex.org/W2079871064","https://openalex.org/W2080097322","https://openalex.org/W2144405395","https://openalex.org/W2151813854","https://openalex.org/W2606796707","https://openalex.org/W2902943087","https://openalex.org/W3007211324","https://openalex.org/W3109438051","https://openalex.org/W3161793875","https://openalex.org/W3195480719","https://openalex.org/W4213115141","https://openalex.org/W4221033551","https://openalex.org/W4309312352","https://openalex.org/W4311472920","https://openalex.org/W4378714036","https://openalex.org/W4380052222","https://openalex.org/W4388215494","https://openalex.org/W6602702067","https://openalex.org/W6682383717","https://openalex.org/W6757023948","https://openalex.org/W6773880708","https://openalex.org/W6809105228"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","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":{"The":[0],"present":[1,37],"paper":[2],"studies":[3],"the":[4,30,34,45,71,75,85],"asymptotic":[5],"and":[6,18,26,33,39,68],"oscillatory":[7,49],"properties":[8],"of":[9,11,87],"solutions":[10],"odd-order":[12],"differential":[13],"equations":[14],"with":[15],"advanced":[16],"arguments":[17],"in":[19,74],"a":[20],"noncanonical":[21],"case.":[22],"By":[23],"providing":[24],"new":[25,40],"effective":[27],"relationships":[28],"between":[29],"corresponding":[31],"function":[32],"solution,":[35],"we":[36],"strict":[38],"criteria":[41],"for":[42],"testing":[43],"whether":[44],"studied":[46],"equation":[47],"exhibits":[48],"behavior":[50],"or":[51],"converges":[52],"to":[53,59,83],"zero.":[54],"Our":[55],"results":[56,72],"contribute":[57],"uniquely":[58],"oscillation":[60],"theory":[61],"by":[62],"presenting":[63],"some":[64],"theorems":[65],"that":[66],"improve":[67],"expand":[69],"upon":[70],"found":[73],"existing":[76],"literature.":[77],"We":[78],"also":[79],"provide":[80],"an":[81],"example":[82],"corroborate":[84],"validity":[86],"our":[88],"proposed":[89],"criteria.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}