{"id":"https://openalex.org/W4366826091","doi":"https://doi.org/10.3390/sym15050970","title":"Existence of Monotone Positive Solutions for Caputo\u2013Hadamard Nonlinear Fractional Differential Equation with Infinite-Point Boundary Value Conditions","display_name":"Existence of Monotone Positive Solutions for Caputo\u2013Hadamard Nonlinear Fractional Differential Equation with Infinite-Point Boundary Value Conditions","publication_year":2023,"publication_date":"2023-04-24","ids":{"openalex":"https://openalex.org/W4366826091","doi":"https://doi.org/10.3390/sym15050970"},"language":"en","primary_location":{"id":"doi:10.3390/sym15050970","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15050970","pdf_url":"https://www.mdpi.com/2073-8994/15/5/970/pdf?version=1682328455","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/2073-8994/15/5/970/pdf?version=1682328455","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042255183","display_name":"Limin Guo","orcid":"https://orcid.org/0000-0002-4779-4181"},"institutions":[{"id":"https://openalex.org/I4210108723","display_name":"Changzhou Institute of Technology","ror":"https://ror.org/020mrfq61","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210108723"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Limin Guo","raw_affiliation_strings":["School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China"],"raw_orcid":"https://orcid.org/0000-0002-4779-4181","affiliations":[{"raw_affiliation_string":"School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China","institution_ids":["https://openalex.org/I4210108723"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049762552","display_name":"Cheng Li","orcid":"https://orcid.org/0000-0003-1018-0087"},"institutions":[{"id":"https://openalex.org/I4210108723","display_name":"Changzhou Institute of Technology","ror":"https://ror.org/020mrfq61","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210108723"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cheng Li","raw_affiliation_strings":["School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China"],"raw_orcid":"https://orcid.org/0000-0003-1018-0087","affiliations":[{"raw_affiliation_string":"School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China","institution_ids":["https://openalex.org/I4210108723"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101707114","display_name":"Jingbo Zhao","orcid":"https://orcid.org/0000-0002-2506-8912"},"institutions":[{"id":"https://openalex.org/I4210108723","display_name":"Changzhou Institute of Technology","ror":"https://ror.org/020mrfq61","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210108723"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingbo Zhao","raw_affiliation_strings":["School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China","institution_ids":["https://openalex.org/I4210108723"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049762552"],"corresponding_institution_ids":["https://openalex.org/I4210108723"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.3696,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87812218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"15","issue":"5","first_page":"970","last_page":"970"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9987999796867371,"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/mathematics","display_name":"Mathematics","score":0.810722827911377},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5914119482040405},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5428661108016968},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5364903211593628},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5235328674316406},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5011539459228516},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47991880774497986},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.45375892519950867},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45306381583213806},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4193713665008545},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4093291759490967},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.12296220660209656},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08158561587333679}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.810722827911377},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5914119482040405},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5428661108016968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5364903211593628},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5235328674316406},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5011539459228516},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47991880774497986},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.45375892519950867},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45306381583213806},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4193713665008545},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4093291759490967},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.12296220660209656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08158561587333679},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym15050970","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15050970","pdf_url":"https://www.mdpi.com/2073-8994/15/5/970/pdf?version=1682328455","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:72e27038cd3d43f688b925a69bc9eb22","is_oa":false,"landing_page_url":"https://doaj.org/article/72e27038cd3d43f688b925a69bc9eb22","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 5, p 970 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15050970","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15050970","pdf_url":"https://www.mdpi.com/2073-8994/15/5/970/pdf?version=1682328455","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":[{"id":"https://openalex.org/G112984136","display_name":null,"funder_award_id":"12272064","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3830447359","display_name":null,"funder_award_id":"12272064, 12101086","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4855929392","display_name":null,"funder_award_id":"12101086","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4366826091.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1971460268","https://openalex.org/W1974336609","https://openalex.org/W1981666988","https://openalex.org/W1991908339","https://openalex.org/W1997024097","https://openalex.org/W2001440053","https://openalex.org/W2002372633","https://openalex.org/W2002769487","https://openalex.org/W2011301580","https://openalex.org/W2014389907","https://openalex.org/W2062879726","https://openalex.org/W2074192813","https://openalex.org/W2074493567","https://openalex.org/W2081344723","https://openalex.org/W2090253689","https://openalex.org/W2130507197","https://openalex.org/W2264699431","https://openalex.org/W2299647821","https://openalex.org/W2323124876","https://openalex.org/W2342233860","https://openalex.org/W2423469018","https://openalex.org/W2510054786","https://openalex.org/W2568590790","https://openalex.org/W2605387555","https://openalex.org/W2728313399","https://openalex.org/W2782178253","https://openalex.org/W2792284196","https://openalex.org/W2801844948","https://openalex.org/W2901128831","https://openalex.org/W2962757073","https://openalex.org/W2963300740","https://openalex.org/W2969584315","https://openalex.org/W2977423024","https://openalex.org/W3005395572","https://openalex.org/W3043511614","https://openalex.org/W3117937071","https://openalex.org/W3121076717","https://openalex.org/W3135634312","https://openalex.org/W3215473531","https://openalex.org/W4200167866","https://openalex.org/W4226324037","https://openalex.org/W4294904757","https://openalex.org/W4364321568","https://openalex.org/W6645530120","https://openalex.org/W6650801531","https://openalex.org/W6651133045","https://openalex.org/W6671031966","https://openalex.org/W6673495298","https://openalex.org/W6679608391","https://openalex.org/W6700845462","https://openalex.org/W6704465321","https://openalex.org/W6804676497"],"related_works":["https://openalex.org/W1982241170","https://openalex.org/W2116282083","https://openalex.org/W2386549147","https://openalex.org/W1978051046","https://openalex.org/W2950361249","https://openalex.org/W1982297468","https://openalex.org/W2016307712","https://openalex.org/W2111217632","https://openalex.org/W4293557899","https://openalex.org/W1585725267"],"abstract_inverted_index":{"Numerical":[0],"solutions":[1,4,17,20,52,82],"and":[2,15,18,42,61],"approximate":[3,16],"of":[5,21,30,64,74,79],"fractional":[6,22,88],"differential":[7,23,89],"equations":[8,24],"have":[9],"been":[10],"studied":[11],"by":[12,53,93],"mathematicians":[13],"recently":[14],"exact":[19],"are":[25,67,91],"obtained":[26,92],"in":[27],"many":[28],"kinds":[29],"ways,":[31],"such":[32],"as":[33],"Lie":[34],"symmetry,":[35],"variational":[36],"method,":[37,41],"the":[38,50,62,72,77,105],"optimal":[39],"ADM":[40],"so":[43],"on.":[44],"In":[45],"this":[46],"paper,":[47],"we":[48],"obtain":[49],"positive":[51,81],"iterative":[54,80,94],"methods":[55,95],"for":[56,83,96],"sum":[57,97],"operators.":[58],"Green\u2019s":[59,65,75],"function":[60,66],"properties":[63,73],"deduced,":[68],"then":[69],"based":[70],"on":[71],"function,":[76],"existence":[78],"a":[84],"nonlinear":[85],"Caputo\u2013Hadamard":[86],"infinite-point":[87],"equation":[90],"operators;":[98],"an":[99],"example":[100],"is":[101],"proved":[102],"to":[103],"illustrate":[104],"main":[106],"result.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
