{"id":"https://openalex.org/W3017965121","doi":"https://doi.org/10.3390/axioms9020044","title":"Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives","display_name":"Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives","publication_year":2020,"publication_date":"2020-04-25","ids":{"openalex":"https://openalex.org/W3017965121","doi":"https://doi.org/10.3390/axioms9020044","mag":"3017965121"},"language":"en","primary_location":{"id":"doi:10.3390/axioms9020044","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9020044","pdf_url":"https://www.mdpi.com/2075-1680/9/2/44/pdf?version=1588134787","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/9/2/44/pdf?version=1588134787","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010112842","display_name":"Muthaiah Subramanian","orcid":"https://orcid.org/0000-0001-5281-0935"},"institutions":[{"id":"https://openalex.org/I4210141018","display_name":"Ramakrishna Mission Vidyalaya","ror":"https://ror.org/042b7qk94","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210141018"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Subramanian Muthaiah","raw_affiliation_strings":["Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, India"],"raw_orcid":"https://orcid.org/0000-0001-5281-0935","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, India","institution_ids":["https://openalex.org/I4210141018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030756029","display_name":"Dumitru B\u01celeanu","orcid":"https://orcid.org/0000-0002-0286-7244"},"institutions":[{"id":"https://openalex.org/I106245021","display_name":"\u00c7ankaya University","ror":"https://ror.org/056wqre19","country_code":"TR","type":"education","lineage":["https://openalex.org/I106245021"]},{"id":"https://openalex.org/I4210142834","display_name":"Institute of Space Science - INFLPR Subsidiary","ror":"https://ror.org/054a6wv56","country_code":"RO","type":"facility","lineage":["https://openalex.org/I4210142834"]}],"countries":["RO","TR"],"is_corresponding":true,"raw_author_name":"Dumitru Baleanu","raw_affiliation_strings":["Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey","Institute of Space Science, 077125 Magurele-Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0002-0286-7244","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey","institution_ids":["https://openalex.org/I106245021"]},{"raw_affiliation_string":"Institute of Space Science, 077125 Magurele-Bucharest, Romania","institution_ids":["https://openalex.org/I4210142834"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030756029"],"corresponding_institution_ids":["https://openalex.org/I106245021","https://openalex.org/I4210142834"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.4209,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.69732737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"2","first_page":"44","last_page":"44"},"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":0.9998000264167786,"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":0.9969000220298767,"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/uniqueness","display_name":"Uniqueness","score":0.8148684501647949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8086553812026978},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7187060117721558},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6998268961906433},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.6104155778884888},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5337247848510742},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5269026756286621},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5163963437080383},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4811174273490906},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45028313994407654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41897153854370117},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.41104161739349365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0677100419998169},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0521242618560791}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8148684501647949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8086553812026978},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7187060117721558},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6998268961906433},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.6104155778884888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5337247848510742},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5269026756286621},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5163963437080383},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4811174273490906},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45028313994407654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41897153854370117},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.41104161739349365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0677100419998169},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0521242618560791},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":3,"locations":[{"id":"doi:10.3390/axioms9020044","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9020044","pdf_url":"https://www.mdpi.com/2075-1680/9/2/44/pdf?version=1588134787","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fa5d3a5a47e24ed19a1b392f02b5361d","is_oa":true,"landing_page_url":"https://doaj.org/article/fa5d3a5a47e24ed19a1b392f02b5361d","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":"Axioms, Vol 9, Iss 2, p 44 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/9/2/44/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms9020044","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":"Axioms; Volume 9; Issue 2; Pages: 44","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms9020044","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9020044","pdf_url":"https://www.mdpi.com/2075-1680/9/2/44/pdf?version=1588134787","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6600000262260437,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3017965121.pdf","grobid_xml":"https://content.openalex.org/works/W3017965121.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1531856058","https://openalex.org/W1584611818","https://openalex.org/W1749659338","https://openalex.org/W1917129599","https://openalex.org/W2038301844","https://openalex.org/W2071593170","https://openalex.org/W2625217045","https://openalex.org/W2775846558","https://openalex.org/W2790741054","https://openalex.org/W2799554099","https://openalex.org/W2799935461","https://openalex.org/W2803031932","https://openalex.org/W2887108880","https://openalex.org/W2893142632","https://openalex.org/W2894332139","https://openalex.org/W2898376695","https://openalex.org/W2905808265","https://openalex.org/W2906852026","https://openalex.org/W2908051436","https://openalex.org/W2939275341","https://openalex.org/W2962843076","https://openalex.org/W2977556127","https://openalex.org/W2982509241","https://openalex.org/W2990082803","https://openalex.org/W2990899766","https://openalex.org/W3171051186","https://openalex.org/W3212808552","https://openalex.org/W4214622128","https://openalex.org/W6751940244","https://openalex.org/W6753502519","https://openalex.org/W6766106392","https://openalex.org/W6768711780","https://openalex.org/W6797391471","https://openalex.org/W6803829363"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4298023222"],"abstract_inverted_index":{"This":[0],"article":[1],"deals":[2],"with":[3,54],"the":[4,7,31,39,47,61,65,69,81],"solutions":[5],"of":[6,15,67,80],"existence":[8],"and":[9,27,42,56],"uniqueness":[10],"for":[11],"a":[12],"new":[13],"class":[14],"boundary":[16,28],"value":[17],"problems":[18],"(BVPs)":[19],"involving":[20,30],"nonlinear":[21],"fractional":[22,33,44],"differential":[23],"equations":[24],"(FDEs),":[25],"inclusions,":[26],"conditions":[29],"generalized":[32],"integral.":[34],"The":[35],"nonlinearity":[36],"relies":[37],"on":[38],"unknown":[40],"function":[41],"its":[43],"derivatives":[45],"in":[46],"lower":[48],"order.":[49],"We":[50,75],"use":[51],"fixed-point":[52],"theorems":[53],"single-valued":[55],"multi-valued":[57],"maps":[58],"to":[59],"obtain":[60],"desired":[62],"results,":[63],"through":[64],"support":[66],"illustrations,":[68],"main":[70],"results":[71],"are":[72],"well":[73],"explained.":[74],"also":[76],"address":[77],"some":[78],"variants":[79],"problem.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-05-01T00:00:00"}
