{"id":"https://openalex.org/W4214626056","doi":"https://doi.org/10.3390/axioms11030096","title":"A Class of Quasilinear Equations with Riemann\u2013Liouville Derivatives and Bounded Operators","display_name":"A Class of Quasilinear Equations with Riemann\u2013Liouville Derivatives and Bounded Operators","publication_year":2022,"publication_date":"2022-02-24","ids":{"openalex":"https://openalex.org/W4214626056","doi":"https://doi.org/10.3390/axioms11030096"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11030096","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030096","pdf_url":"https://www.mdpi.com/2075-1680/11/3/96/pdf?version=1645784910","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/2075-1680/11/3/96/pdf?version=1645784910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073475467","display_name":"\u0412. \u0415. \u0424\u0435\u0434\u043e\u0440\u043e\u0432","orcid":"https://orcid.org/0000-0002-0787-3272"},"institutions":[{"id":"https://openalex.org/I107640659","display_name":"South Ural State University","ror":"https://ror.org/03sfk2504","country_code":"RU","type":"education","lineage":["https://openalex.org/I107640659"]},{"id":"https://openalex.org/I137211346","display_name":"Chelyabinsk State University","ror":"https://ror.org/04s36qm86","country_code":"RU","type":"education","lineage":["https://openalex.org/I137211346"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Vladimir E. Fedorov","raw_affiliation_strings":["Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, Russia","Laboratory of Functional Materials, South Ural State University (National Research University), Lenin Av., 76, 454080 Chelyabinsk, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, Russia","institution_ids":["https://openalex.org/I137211346"]},{"raw_affiliation_string":"Laboratory of Functional Materials, South Ural State University (National Research University), Lenin Av., 76, 454080 Chelyabinsk, Russia","institution_ids":["https://openalex.org/I107640659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027723754","display_name":"Mikhail M. Turov","orcid":"https://orcid.org/0000-0003-4075-5099"},"institutions":[{"id":"https://openalex.org/I137211346","display_name":"Chelyabinsk State University","ror":"https://ror.org/04s36qm86","country_code":"RU","type":"education","lineage":["https://openalex.org/I137211346"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Mikhail M. Turov","raw_affiliation_strings":["Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St., 129, 454001 Chelyabinsk, Russia","institution_ids":["https://openalex.org/I137211346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033764668","display_name":"B. T. Kien","orcid":"https://orcid.org/0000-0001-8370-7009"},"institutions":[{"id":"https://openalex.org/I4210148301","display_name":"Institute of Mathematics","ror":"https://ror.org/04jr71r83","country_code":"VN","type":"facility","lineage":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]},{"id":"https://openalex.org/I70349855","display_name":"Vietnam Academy of Science and Technology","ror":"https://ror.org/02wsd5p50","country_code":"VN","type":"funder","lineage":["https://openalex.org/I70349855"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Bui Trong Kien","raw_affiliation_strings":["Department of Optimization and Control Theory, Institute of Mathematics of the Vietnam Academy of Sciences and Technologies, 8 Hoang Quoc Viet Road, Caugiay District, Hanoi 10307, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Optimization and Control Theory, Institute of Mathematics of the Vietnam Academy of Sciences and Technologies, 8 Hoang Quoc Viet Road, Caugiay District, Hanoi 10307, Vietnam","institution_ids":["https://openalex.org/I70349855","https://openalex.org/I4210148301"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073475467"],"corresponding_institution_ids":["https://openalex.org/I107640659","https://openalex.org/I137211346"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.1355,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85972518,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"3","first_page":"96","last_page":"96"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9998999834060669,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9998999834060669,"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":0.9991000294685364,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9983000159263611,"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/mathematics","display_name":"Mathematics","score":0.8143079280853271},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6366421580314636},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5722543001174927},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5487670302391052},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5404267311096191},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4842686057090759},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46897730231285095},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4659233093261719},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4453479051589966},{"id":"https://openalex.org/keywords/semi-elliptic-operator","display_name":"Semi-elliptic operator","score":0.421015202999115},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41408252716064453},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.41060739755630493},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.407375305891037},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.2952340841293335}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8143079280853271},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6366421580314636},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5722543001174927},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5487670302391052},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5404267311096191},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4842686057090759},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46897730231285095},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4659233093261719},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4453479051589966},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.421015202999115},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41408252716064453},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.41060739755630493},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.407375305891037},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.2952340841293335},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11030096","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030096","pdf_url":"https://www.mdpi.com/2075-1680/11/3/96/pdf?version=1645784910","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:d3c8a62027bb4bbfa709ce8d9fd25a92","is_oa":true,"landing_page_url":"https://doaj.org/article/d3c8a62027bb4bbfa709ce8d9fd25a92","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":"Axioms, Vol 11, Iss 3, p 96 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/3/96/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11030096","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 11; Issue 3; Pages: 96","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11030096","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030096","pdf_url":"https://www.mdpi.com/2075-1680/11/3/96/pdf?version=1645784910","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":[],"awards":[{"id":"https://openalex.org/G2093727313","display_name":null,"funder_award_id":"21-51-54003","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4214626056.pdf","grobid_xml":"https://content.openalex.org/works/W4214626056.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1454301189","https://openalex.org/W1971200514","https://openalex.org/W2236672491","https://openalex.org/W2973452964","https://openalex.org/W3047000935","https://openalex.org/W3111160211","https://openalex.org/W3204860109","https://openalex.org/W4206116457","https://openalex.org/W4238980657","https://openalex.org/W4256340197","https://openalex.org/W4324121438","https://openalex.org/W6689945203","https://openalex.org/W6768095374"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2318923278","https://openalex.org/W2999850718","https://openalex.org/W4287548472","https://openalex.org/W2548037050"],"abstract_inverted_index":{"The":[0,65,103],"existence":[1],"and":[2,28,43],"uniqueness":[3],"of":[4,60,75,85],"a":[5,73],"local":[6],"solution":[7],"is":[8,37,69,112],"proved":[9],"for":[10],"the":[11,35,53,58,61,100,107],"incomplete":[12],"Cauchy":[13],"type":[14],"problem":[15],"to":[16,39,71,79,93,114,119],"multi-term":[17],"quasilinear":[18],"fractional":[19,48,55,63],"differential":[20,89,110],"equations":[21,82,111],"in":[22,34,106],"Banach":[23],"spaces":[24],"with":[25,83,91,117],"Riemann\u2013Liouville":[26],"derivatives":[27],"bounded":[29],"operators":[30,98],"at":[31,99],"them.":[32],"Nonlinearity":[33],"equation":[36],"assumed":[38,113],"be":[40,115],"Lipschitz":[41],"continuous":[42],"dependent":[44],"on":[45],"lower":[46],"order":[47,59,81],"derivatives,":[49],"which":[50],"orders":[51],"have":[52],"same":[54],"part":[56],"as":[57,96],"highest":[62],"derivative.":[64],"obtained":[66],"abstract":[67],"result":[68],"applied":[70],"study":[72],"class":[74],"initial-boundary":[76],"value":[77],"problems":[78],"time-fractional":[80,101],"polynomials":[84],"an":[86],"elliptic":[87],"self-adjoint":[88],"operator":[90,105],"respect":[92,118],"spatial":[94],"variables":[95],"linear":[97],"derivatives.":[102],"nonlinear":[104],"considered":[108],"partial":[109],"smooth":[116],"phase":[120],"variables.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-23T07:41:27.035349","created_date":"2022-03-02T00:00:00"}
