{"id":"https://openalex.org/W3210099358","doi":"https://doi.org/10.3390/axioms10040277","title":"Sequential Riemann\u2013Liouville and Hadamard\u2013Caputo Fractional Differential Equation with Iterated Fractional Integrals Conditions","display_name":"Sequential Riemann\u2013Liouville and Hadamard\u2013Caputo Fractional Differential Equation with Iterated Fractional Integrals Conditions","publication_year":2021,"publication_date":"2021-10-27","ids":{"openalex":"https://openalex.org/W3210099358","doi":"https://doi.org/10.3390/axioms10040277","mag":"3210099358"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10040277","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040277","pdf_url":"https://www.mdpi.com/2075-1680/10/4/277/pdf?version=1636010903","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/2075-1680/10/4/277/pdf?version=1636010903","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086599287","display_name":"Sotiris K. Ntouyas","orcid":"https://orcid.org/0000-0002-7695-2118"},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]},{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["GR","SA"],"is_corresponding":false,"raw_author_name":"Sotiris K. Ntouyas","raw_affiliation_strings":["Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece","Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]},{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025773906","display_name":"Surang Sitho","orcid":null},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Surang Sitho","raw_affiliation_strings":["Department of Social and Applied Science, College of Industrial Technology, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Department of Social and Applied Science, College of Industrial Technology, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Social and Applied Science, College of Industrial Technology, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Department of Social and Applied Science, College of Industrial Technology, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054010275","display_name":"Teerasak Khoployklang","orcid":"https://orcid.org/0000-0003-0411-9052"},"institutions":[{"id":"https://openalex.org/I95579309","display_name":"Chandrakasem Rajabhat University","ror":"https://ror.org/02g6rcz57","country_code":"TH","type":"education","lineage":["https://openalex.org/I95579309"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Teerasak Khoployklang","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Chandrakasem Rajabhat University, Bangkok 10900, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Chandrakasem Rajabhat University, Bangkok 10900, Thailand","institution_ids":["https://openalex.org/I95579309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051443783","display_name":"Jessada Tariboon","orcid":"https://orcid.org/0000-0001-8185-3539"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Jessada Tariboon","raw_affiliation_strings":["Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"affiliations":[{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5051443783"],"corresponding_institution_ids":["https://openalex.org/I82828225"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5374,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63583394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"10","issue":"4","first_page":"277","last_page":"277"},"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":0.9995999932289124,"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":0.9921000003814697,"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":0.8313889503479004},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7224029302597046},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.7068064212799072},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5934244990348816},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5826174020767212},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5797250270843506},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4914897680282593},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.48477596044540405},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45913106203079224},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4566878080368042},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44779300689697266},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43700212240219116},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3521423935890198}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8313889503479004},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7224029302597046},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.7068064212799072},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5934244990348816},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5826174020767212},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5797250270843506},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4914897680282593},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.48477596044540405},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45913106203079224},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4566878080368042},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44779300689697266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43700212240219116},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3521423935890198},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/axioms10040277","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040277","pdf_url":"https://www.mdpi.com/2075-1680/10/4/277/pdf?version=1636010903","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:58c797969fea41488dcd46eb5f6b6284","is_oa":true,"landing_page_url":"https://doaj.org/article/58c797969fea41488dcd46eb5f6b6284","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 10, Iss 4, p 277 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/10/4/277/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms10040277","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 10; Issue 4; Pages: 277","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms10040277","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040277","pdf_url":"https://www.mdpi.com/2075-1680/10/4/277/pdf?version=1636010903","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/G2291743297","display_name":null,"funder_award_id":"KMUTNB-62-KNOW-41","funder_id":"https://openalex.org/F4320324344","funder_display_name":"King Mongkut's University of Technology North Bangkok"}],"funders":[{"id":"https://openalex.org/F4320324344","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3210099358.pdf","grobid_xml":"https://content.openalex.org/works/W3210099358.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W604143053","https://openalex.org/W833693987","https://openalex.org/W1528987510","https://openalex.org/W1978866646","https://openalex.org/W1981459842","https://openalex.org/W2010114544","https://openalex.org/W2064037905","https://openalex.org/W2083559699","https://openalex.org/W2137273002","https://openalex.org/W2299647821","https://openalex.org/W2403228298","https://openalex.org/W2595653665","https://openalex.org/W2784017377","https://openalex.org/W2895880266","https://openalex.org/W2900673459","https://openalex.org/W2902496823","https://openalex.org/W2910215967","https://openalex.org/W3012772895","https://openalex.org/W3120644059","https://openalex.org/W3190893591","https://openalex.org/W3191996400","https://openalex.org/W3192060108","https://openalex.org/W3194995474","https://openalex.org/W4237844826","https://openalex.org/W4247953052","https://openalex.org/W4254874516","https://openalex.org/W6756576382","https://openalex.org/W6758666010","https://openalex.org/W6775432495"],"related_works":["https://openalex.org/W2111217632","https://openalex.org/W4293557899","https://openalex.org/W2002150947","https://openalex.org/W2081997106","https://openalex.org/W4387722500","https://openalex.org/W2005448961","https://openalex.org/W2846516035","https://openalex.org/W1987841878","https://openalex.org/W2716174782","https://openalex.org/W4249977926"],"abstract_inverted_index":{"In":[0],"the":[1,6,29,44,48,92,104,109],"present":[2],"research,":[3],"we":[4,27,54],"initiate":[5],"study":[7,79],"of":[8,43,58,71],"boundary":[9,24,112],"value":[10,113],"problems":[11,114],"for":[12,115],"sequential":[13],"Riemann\u2013Liouville":[14],"and":[15,67,107],"Hadamard\u2013Caputo":[16],"fractional":[17,22,116],"derivatives,":[18],"supplemented":[19],"with":[20],"iterated":[21],"integral":[23],"conditions.":[25],"Firstly,":[26],"convert":[28],"given":[30,45,105],"nonlinear":[31],"problem":[32,37],"into":[33],"a":[34,40,56,94],"fixed":[35,49,59],"point":[36,50,60],"by":[38],"considering":[39],"linear":[41],"variant":[42],"problem.":[46],"Once":[47],"operator":[51],"is":[52,97],"available,":[53],"use":[55],"variety":[57],"theorems":[61],"to":[62],"establish":[63],"results":[64,87,100],"regarding":[65],"existence":[66],"uniqueness.":[68],"Some":[69],"properties":[70],"iteration":[72],"that":[73],"will":[74],"be":[75],"used":[76],"in":[77,103],"our":[78,85],"are":[80,88,101],"also":[81,89],"discussed.":[82],"Examples":[83],"illustrating":[84],"main":[86],"constructed.":[90],"At":[91],"end,":[93],"brief":[95],"conclusion":[96],"given.":[98],"Our":[99],"new":[102],"configuration":[106],"enrich":[108],"literature":[110],"on":[111],"differential":[117],"equations.":[118]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}