{"id":"https://openalex.org/W4283025025","doi":"https://doi.org/10.1155/2022/8113760","title":"Chaotic Phenomena and Oscillations in Dynamical Behaviour of Financial System via Fractional Calculus","display_name":"Chaotic Phenomena and Oscillations in Dynamical Behaviour of Financial System via Fractional Calculus","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4283025025","doi":"https://doi.org/10.1155/2022/8113760"},"language":"en","primary_location":{"id":"doi:10.1155/2022/8113760","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8113760","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8113760.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2022/8113760.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030166628","display_name":"Zahir Shah","orcid":"https://orcid.org/0000-0002-5539-4225"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zahir Shah","raw_affiliation_strings":["Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, KPK, Pakistan","Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, KPK"],"raw_orcid":"https://orcid.org/0000-0002-5539-4225","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, KPK, Pakistan","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, KPK","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066581129","display_name":"Ebenezer Bonyah","orcid":"https://orcid.org/0000-0003-0808-4504"},"institutions":[{"id":"https://openalex.org/I145876445","display_name":"University of Education, Winneba","ror":"https://ror.org/00y1ekh28","country_code":"GH","type":"education","lineage":["https://openalex.org/I145876445"]}],"countries":["GH"],"is_corresponding":true,"raw_author_name":"Ebenezer Bonyah","raw_affiliation_strings":["Department of Mathematics Education, University of Education Winneba Kumasi-(Kumasicompus), Kumasi 00233, Ghana","Department of Mathematics Education, University of Education Winneba Kumasi-(Kumasicompus), Kumasi 00233"],"raw_orcid":"https://orcid.org/0000-0003-0808-4504","affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, University of Education Winneba Kumasi-(Kumasicompus), Kumasi 00233, Ghana","institution_ids":["https://openalex.org/I145876445"]},{"raw_affiliation_string":"Department of Mathematics Education, University of Education Winneba Kumasi-(Kumasicompus), Kumasi 00233","institution_ids":["https://openalex.org/I145876445"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046896093","display_name":"Ebraheem Alzahrani","orcid":"https://orcid.org/0000-0003-2413-0355"},"institutions":[{"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":["SA"],"is_corresponding":false,"raw_author_name":"Ebraheem Alzahrani","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589"],"raw_orcid":"https://orcid.org/0000-0003-2413-0355","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058744595","display_name":"Rashid Jan","orcid":"https://orcid.org/0000-0001-9709-7045"},"institutions":[{"id":"https://openalex.org/I4210142599","display_name":"University of Swabi","ror":"https://ror.org/04ez8az68","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210142599"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rashid Jan","raw_affiliation_strings":["Department of Mathematics, University of Swabi, Swabi 23561, KPK, Pakistan","Department of Mathematics, University of Swabi, Swabi 23561, KPK"],"raw_orcid":"https://orcid.org/0000-0001-9709-7045","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Swabi, Swabi 23561, KPK, Pakistan","institution_ids":["https://openalex.org/I4210142599"]},{"raw_affiliation_string":"Department of Mathematics, University of Swabi, Swabi 23561, KPK","institution_ids":["https://openalex.org/I4210142599"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031599777","display_name":"Nasser Aedh Alreshidi","orcid":"https://orcid.org/0000-0003-0666-9269"},"institutions":[{"id":"https://openalex.org/I118590987","display_name":"Northern Border University","ror":"https://ror.org/03j9tzj20","country_code":"SA","type":"education","lineage":["https://openalex.org/I118590987"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Nasser Aedh Alreshidi","raw_affiliation_strings":["Department of Mathematic College of Science Northern Border University, Arar 73222, Saudi Arabia","Department of Mathematic College of Science Northern Border University, Arar 73222"],"raw_orcid":"https://orcid.org/0000-0003-0666-9269","affiliations":[{"raw_affiliation_string":"Department of Mathematic College of Science Northern Border University, Arar 73222, Saudi Arabia","institution_ids":["https://openalex.org/I118590987"]},{"raw_affiliation_string":"Department of Mathematic College of Science Northern Border University, Arar 73222","institution_ids":["https://openalex.org/I118590987"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5066581129"],"corresponding_institution_ids":["https://openalex.org/I145876445"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":11.9536,"has_fulltext":true,"cited_by_count":46,"citation_normalized_percentile":{"value":0.98261393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"2022","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9940000176429749,"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/T10244","display_name":"Chaos control and synchronization","score":0.9776999950408936,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6750658750534058},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6490159630775452},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5108184814453125},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.42531803250312805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.409923255443573},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39844006299972534},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.378680557012558},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33759093284606934},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2629525065422058},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10477930307388306},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10053348541259766},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07658502459526062},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05739736557006836}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6750658750534058},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6490159630775452},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5108184814453125},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.42531803250312805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.409923255443573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39844006299972534},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.378680557012558},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33759093284606934},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2629525065422058},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10477930307388306},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10053348541259766},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07658502459526062},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05739736557006836},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/8113760","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8113760","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8113760.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:8113760","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2022/8113760.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:0ebe09b59aae49c39aaea0f1ca781678","is_oa":false,"landing_page_url":"https://doaj.org/article/0ebe09b59aae49c39aaea0f1ca781678","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":"Complexity, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/8113760","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8113760","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/8113760.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.5699999928474426}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283025025.pdf","grobid_xml":"https://content.openalex.org/works/W4283025025.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W978665728","https://openalex.org/W1966877875","https://openalex.org/W1967510217","https://openalex.org/W1970416408","https://openalex.org/W1972345373","https://openalex.org/W1976451792","https://openalex.org/W1984257705","https://openalex.org/W1996411883","https://openalex.org/W2001194598","https://openalex.org/W2012613827","https://openalex.org/W2014105256","https://openalex.org/W2052188624","https://openalex.org/W2054151158","https://openalex.org/W2064371875","https://openalex.org/W2094551465","https://openalex.org/W2344298532","https://openalex.org/W2443361655","https://openalex.org/W2584321806","https://openalex.org/W3006333292","https://openalex.org/W3048888343","https://openalex.org/W3080278394","https://openalex.org/W3080954384","https://openalex.org/W3092136141","https://openalex.org/W3135709622","https://openalex.org/W3139323790","https://openalex.org/W3159624917","https://openalex.org/W4237227322"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W2004708907","https://openalex.org/W4246784705","https://openalex.org/W3121927021","https://openalex.org/W2377429601","https://openalex.org/W4390948881","https://openalex.org/W1537973975","https://openalex.org/W4312960772"],"abstract_inverted_index":{"In":[0],"this":[1],"research":[2],"work,":[3],"we":[4,84],"formulate":[5],"the":[6,9,13,18,29,42,55,60,67,81,86,92,97,102,107,113,119,131,134],"phenomena":[7],"of":[8,21,28,45,54,62,88,101,109,121,133],"financial":[10,136],"system":[11,103],"in":[12,80],"fractional":[14,31,47,124],"framework":[15],"to":[16],"describe":[17],"complex":[19,99],"nature":[20],"finance.":[22],"The":[23,49,94],"basic":[24],"definitions":[25],"and":[26,51,77,126],"ideas":[27],"Caputo\u2010Fabrizio":[30],"operator":[32],"are":[33,104],"listed.":[34],"We":[35,69],"introduce":[36],"a":[37],"novel":[38],"numerical":[39],"technique":[40],"for":[41,96],"dynamical":[43],"behaviour":[44,53,79,100],"our":[46],"model.":[48,68,93],"oscillatory":[50,76],"chaotic":[52,78],"model":[56],"is":[57],"studied":[58],"with":[59,106],"variation":[61],"various":[63],"input":[64,127],"parameters":[65,111,128],"on":[66,91,112],"have":[70],"shown":[71],"that":[72,118],"there":[73],"exists":[74],"strong":[75],"system;":[82],"moreover,":[83],"highlighted":[85],"impact":[87,108],"fractional\u2010order":[89],"parameter":[90],"conditions":[95],"local":[98],"analyzed":[105],"certain":[110],"macroeconomic.":[114],"Our":[115],"findings":[116],"suggest":[117],"values":[120],"initial":[122],"conditions,":[123],"order,":[125],"can":[129],"lessen":[130],"chaos":[132],"proposed":[135],"system.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
