{"id":"https://openalex.org/W4416601564","doi":"https://doi.org/10.3934/math.20251197","title":"Eigenvalue ratios for the conformable fractional vibrating string equations with single-well densities","display_name":"Eigenvalue ratios for the conformable fractional vibrating string equations with single-well densities","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4416601564","doi":"https://doi.org/10.3934/math.20251197"},"language":"en","primary_location":{"id":"doi:10.3934/math.20251197","doi":"https://doi.org/10.3934/math.20251197","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20251197","pdf_url":"http://www.aimspress.com/aimspress-data/math/2025/11/PDF/math-10-11-1197.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://www.aimspress.com/aimspress-data/math/2025/11/PDF/math-10-11-1197.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112998673","display_name":"Mengze Gu","orcid":"https://orcid.org/0009-0007-1624-5044","observed_orcids":["https://orcid.org/0009-0007-1624-5044"]},"institutions":[{"id":"https://openalex.org/I3130607311","display_name":"Changsha Normal University","ror":"https://ror.org/02sqk3z62","country_code":"CN","type":"education","lineage":["https://openalex.org/I3130607311"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mengze Gu","raw_affiliation_strings":["School of Mathematics and Science, Changsha Normal University, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Science, Changsha Normal University, Changsha 410083, China","institution_ids":["https://openalex.org/I3130607311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112998673"],"corresponding_institution_ids":["https://openalex.org/I3130607311"],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":0.694,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55543123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"10","issue":"11","first_page":"27235","last_page":"27246"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.004399999976158142,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.004100000020116568,"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/eigenvalue-ratio","display_name":"eigenvalue ratio","score":0.8550000190734863},{"id":"https://openalex.org/keywords/conformable-fractional-derivative","display_name":"conformable fractional derivative","score":0.9160000085830688},{"id":"https://openalex.org/keywords/vibrating-string","display_name":"string vibration","score":0.6769999861717224},{"id":"https://openalex.org/keywords/sturm-liouville-problems","display_name":"Sturm-Liouville problems","score":0.9490000009536743},{"id":"https://openalex.org/keywords/eigenvalue-inequalities","display_name":"eigenvalue inequalities","score":0.9139999747276306},{"id":"https://openalex.org/keywords/eigenvalue-upper-bounds","display_name":"upper bounds on eigenvalues","score":0.5789999961853027},{"id":"https://openalex.org/keywords/fractional-sturm-liouville-problem","display_name":"fractional Sturm-Liouville problem","score":0.6320000290870667}],"concepts":[{"id":"https://openalex.org/C86072612","wikidata":"https://www.wikidata.org/wiki/Q5160239","display_name":"Conformable matrix","level":2,"score":0.975600004196167},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.782800018787384},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6603000164031982},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.6495000123977661},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5825999975204468},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5627999901771545},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5094000101089478},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4977000057697296},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46050000190734863},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.32519999146461487},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.3163999915122986},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31220000982284546},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2985000014305115},{"id":"https://openalex.org/C2778738651","wikidata":"https://www.wikidata.org/wiki/Q16546687","display_name":"Novelty","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.28139999508857727},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2597000002861023},{"id":"https://openalex.org/C24743483","wikidata":"https://www.wikidata.org/wiki/Q1154848","display_name":"Potential theory","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/math.20251197","doi":"https://doi.org/10.3934/math.20251197","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20251197","pdf_url":"http://www.aimspress.com/aimspress-data/math/2025/11/PDF/math-10-11-1197.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/math.20251197","doi":"https://doi.org/10.3934/math.20251197","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20251197","pdf_url":"http://www.aimspress.com/aimspress-data/math/2025/11/PDF/math-10-11-1197.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416601564.pdf","grobid_xml":"https://content.openalex.org/works/W4416601564.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1494263571","https://openalex.org/W1990348216","https://openalex.org/W2051186530","https://openalex.org/W2063067239","https://openalex.org/W2080931732","https://openalex.org/W2092434220","https://openalex.org/W2192948312","https://openalex.org/W2472805732","https://openalex.org/W2740597683","https://openalex.org/W2946094287","https://openalex.org/W3204333618","https://openalex.org/W3208662270"],"related_works":["https://openalex.org/W3213484068","https://openalex.org/W3204333618","https://openalex.org/W3214356764","https://openalex.org/W1494263571","https://openalex.org/W2092434220","https://openalex.org/W246319209","https://openalex.org/W7164414352","https://openalex.org/W4386620333","https://openalex.org/W2754379126","https://openalex.org/W7171006877"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,44,67],"investigated":[4],"in":[5,86],"a":[6],"class":[7],"of":[8,21,33,41],"Sturm-Liouville":[9],"vibrating":[10],"string":[11],"problems":[12],"involving":[13],"conformable":[14,95],"fractional":[15,96],"derivatives":[16],"and":[17,73],"studied":[18],"the":[19,26,29,37,47,52,76,79,88,94],"behavior":[20],"their":[22],"eigenvalue":[23,53,91],"ratios.":[24],"Under":[25],"assumptions":[27],"that":[28,69],"potential":[30,80],"function":[31,39],"is":[32,40,81],"single-barrier":[34],"type":[35],"or":[36,78],"density":[38,77],"single-well":[42],"type,":[43],"rigorously":[45],"established":[46],"optimal":[48],"upper":[49],"bound":[50],"for":[51],"ratios":[54],"$":[55],"\\lambda_n":[56],"/":[57],"\\lambda_m":[58],"$,":[59],"namely$":[60],"\\frac{\\lambda_n}{\\lambda_m}":[61],"\\le":[62],"\\left(\\frac{n}{m}\\right)^2":[63],"\\quad":[64],"(n>m).":[65],"$Moreover,":[66],"showed":[68],"equality":[70],"holds":[71],"if":[72,75],"only":[74],"constant.":[82],"Our":[83],"novelty":[84],"was":[85],"extending":[87],"classical":[89],"Sturm\u2013Liouville":[90],"inequalities":[92],"to":[93],"setting.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2025-11-25T00:00:00"}