{"id":"https://openalex.org/W4408505320","doi":"https://doi.org/10.3390/sym17030446","title":"On the Oscillatory Behavior of a Class of Mixed Fractional-Order Nonlinear Differential Equations","display_name":"On the Oscillatory Behavior of a Class of Mixed Fractional-Order Nonlinear Differential Equations","publication_year":2025,"publication_date":"2025-03-17","ids":{"openalex":"https://openalex.org/W4408505320","doi":"https://doi.org/10.3390/sym17030446"},"language":"en","primary_location":{"id":"doi:10.3390/sym17030446","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030446","pdf_url":"https://www.mdpi.com/2073-8994/17/3/446/pdf?version=1742205243","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/3/446/pdf?version=1742205243","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014915773","display_name":"George E. Chatzarakis","orcid":"https://orcid.org/0000-0002-0477-1895"},"institutions":[{"id":"https://openalex.org/I254421610","display_name":"School of Pedagogical and Technological Education","ror":"https://ror.org/04v3r9z94","country_code":"GR","type":"education","lineage":["https://openalex.org/I254421610"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"George E. Chatzarakis","raw_affiliation_strings":["Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE), 15122 Athens, Greece"],"raw_orcid":"https://orcid.org/0000-0002-0477-1895","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE), 15122 Athens, Greece","institution_ids":["https://openalex.org/I254421610"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029695307","display_name":"N. Nagajothi","orcid":"https://orcid.org/0000-0002-3635-2396"},"institutions":[{"id":"https://openalex.org/I4210088592","display_name":"Goverment Siddha Medical College","ror":"https://ror.org/00997qd48","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210088592"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"N. Nagajothi","raw_affiliation_strings":["Department of Mathematics, Nandha Engineering College, Erode 638 052, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0002-3635-2396","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nandha Engineering College, Erode 638 052, Tamil Nadu, India","institution_ids":["https://openalex.org/I4210088592"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012058684","display_name":"M. Deepa","orcid":"https://orcid.org/0000-0001-6210-4911"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Deepa","raw_affiliation_strings":["Department of Mathematics, Pavai Arts and Science College for Women, Rasipuram 637 401, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pavai Arts and Science College for Women, Rasipuram 637 401, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017451919","display_name":"V. Sadhasivam","orcid":"https://orcid.org/0000-0001-5333-0001"},"institutions":[{"id":"https://openalex.org/I117381506","display_name":"Thiruvalluvar University","ror":"https://ror.org/0255nn983","country_code":"IN","type":"education","lineage":["https://openalex.org/I117381506"]},{"id":"https://openalex.org/I141431873","display_name":"Periyar University","ror":"https://ror.org/05crs8s98","country_code":"IN","type":"education","lineage":["https://openalex.org/I141431873"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vadivel Sadhasivam","raw_affiliation_strings":["Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affiliated to Periyar University), Namakkal Dt., Rasipuram 637 401, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affiliated to Periyar University), Namakkal Dt., Rasipuram 637 401, Tamil Nadu, India","institution_ids":["https://openalex.org/I117381506","https://openalex.org/I141431873"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5014915773"],"corresponding_institution_ids":["https://openalex.org/I254421610"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.8091,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6448423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"3","first_page":"446","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9986000061035156,"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":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6677998304367065},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6385949850082397},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5882930755615234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5384551882743835},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45937976241111755},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43895381689071655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39902329444885254},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26527613401412964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1604919135570526},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0910041332244873}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6677998304367065},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6385949850082397},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5882930755615234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5384551882743835},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45937976241111755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43895381689071655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39902329444885254},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26527613401412964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1604919135570526},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0910041332244873},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17030446","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030446","pdf_url":"https://www.mdpi.com/2073-8994/17/3/446/pdf?version=1742205243","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"}],"best_oa_location":{"id":"doi:10.3390/sym17030446","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030446","pdf_url":"https://www.mdpi.com/2073-8994/17/3/446/pdf?version=1742205243","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/W4408505320.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W604143053","https://openalex.org/W2050200852","https://openalex.org/W2063067239","https://openalex.org/W2063631565","https://openalex.org/W2080222367","https://openalex.org/W2080931732","https://openalex.org/W2099721887","https://openalex.org/W2101922585","https://openalex.org/W2103787807","https://openalex.org/W2128683301","https://openalex.org/W2143954610","https://openalex.org/W2472805732","https://openalex.org/W2514056648","https://openalex.org/W2523984925","https://openalex.org/W2543400132","https://openalex.org/W2556794753","https://openalex.org/W3039433601","https://openalex.org/W3118842880","https://openalex.org/W4238387230","https://openalex.org/W4247953052","https://openalex.org/W4256340197","https://openalex.org/W4309731561","https://openalex.org/W4387313483","https://openalex.org/W4392544389","https://openalex.org/W4401254332","https://openalex.org/W4404490715","https://openalex.org/W6726263167","https://openalex.org/W6727732392","https://openalex.org/W6728807580","https://openalex.org/W6730339970","https://openalex.org/W6873651441"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W2382250648","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158","https://openalex.org/W4379507409","https://openalex.org/W2066331732","https://openalex.org/W2561874146","https://openalex.org/W2348093013"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,17,31,44,60,63,68,73,94,99,102],"oscillatory":[4,32,53],"behavior":[5,33,54],"of":[6,9,34,101],"a":[7,26,47],"class":[8],"mixed":[10],"fractional-order":[11],"nonlinear":[12],"differential":[13,57],"equations":[14],"incorporating":[15],"both":[16],"Liouville":[18],"right-sided":[19],"and":[20,72,84,97],"conformable":[21],"fractional":[22,56],"derivatives.":[23],"Symmetry":[24],"plays":[25],"key":[27],"role":[28],"in":[29,55,62],"understanding":[30],"these":[35],"systems.":[36],"The":[37],"motivation":[38],"behind":[39],"this":[40],"study":[41],"arises":[42],"from":[43],"need":[45],"for":[46],"more":[48],"generalized":[49,69],"framework":[50],"to":[51,92],"analyze":[52],"equations,":[58],"bridging":[59],"gap":[61],"existing":[64],"literature.":[65],"By":[66],"employing":[67],"Riccati":[70],"technique":[71],"integral":[74],"averaging":[75],"method,":[76],"we":[77],"establish":[78],"new":[79],"oscillation":[80],"criteria":[81],"that":[82],"extend":[83],"refine":[85],"previous":[86],"results.":[87],"Illustrative":[88],"examples":[89],"are":[90],"provided":[91],"validate":[93],"theoretical":[95],"findings":[96],"highlight":[98],"effectiveness":[100],"proposed":[103],"methods.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
