{"id":"https://openalex.org/W2803524865","doi":"https://doi.org/10.3390/e20050384","title":"Chaotic Attractors with Fractional Conformable Derivatives in the Liouville\u2013Caputo Sense and Its Dynamical Behaviors","display_name":"Chaotic Attractors with Fractional Conformable Derivatives in the Liouville\u2013Caputo Sense and Its Dynamical Behaviors","publication_year":2018,"publication_date":"2018-05-20","ids":{"openalex":"https://openalex.org/W2803524865","doi":"https://doi.org/10.3390/e20050384","mag":"2803524865","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265474"},"language":"en","primary_location":{"id":"doi:10.3390/e20050384","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20050384","pdf_url":"https://www.mdpi.com/1099-4300/20/5/384/pdf?version=1526807882","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/5/384/pdf?version=1526807882","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029501554","display_name":"J.E. Sol\u00eds-P\u00e9rez","orcid":"https://orcid.org/0000-0002-4729-9949"},"institutions":[{"id":"https://openalex.org/I4210090124","display_name":"Tecnol\u00f3gico Nacional de M\u00e9xico","ror":"https://ror.org/00davry38","country_code":"MX","type":"government","lineage":["https://openalex.org/I1302736544","https://openalex.org/I4210090124","https://openalex.org/I4405258672"]},{"id":"https://openalex.org/I4210138655","display_name":"Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico","ror":"https://ror.org/0314ecq26","country_code":"MX","type":"facility","lineage":["https://openalex.org/I4210138655"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jes\u00fas Emmanuel Sol\u00eds P\u00e9rez","raw_affiliation_strings":["Tecnol\u00f3gico Nacional de M\u00e9xico/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico"],"affiliations":[{"raw_affiliation_string":"Tecnol\u00f3gico Nacional de M\u00e9xico/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico","institution_ids":["https://openalex.org/I4210138655","https://openalex.org/I4210090124"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016818633","display_name":"J. F. G\u00f3mez\u2010Aguilar","orcid":"https://orcid.org/0000-0001-9403-3767"},"institutions":[{"id":"https://openalex.org/I4210090124","display_name":"Tecnol\u00f3gico Nacional de M\u00e9xico","ror":"https://ror.org/00davry38","country_code":"MX","type":"government","lineage":["https://openalex.org/I1302736544","https://openalex.org/I4210090124","https://openalex.org/I4405258672"]},{"id":"https://openalex.org/I4210138655","display_name":"Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico","ror":"https://ror.org/0314ecq26","country_code":"MX","type":"facility","lineage":["https://openalex.org/I4210138655"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Francisco G\u00f3mez-Aguilar","raw_affiliation_strings":["CONACyT-Tecnol\u00f3gico Nacional de M\u00e9xico/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico"],"affiliations":[{"raw_affiliation_string":"CONACyT-Tecnol\u00f3gico Nacional de M\u00e9xico/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Mexico","institution_ids":["https://openalex.org/I4210138655","https://openalex.org/I4210090124"]}]},{"author_position":"middle","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":false,"raw_author_name":"Dumitru Baleanu","raw_affiliation_strings":["Department of Mathematics, Faculty of Art and Sciences, Cankaya University, 06530 Ankara, Turkey","Institute of Space Sciences, P.O. Box, MG-23, R 76900 Magurele-Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Art and Sciences, Cankaya University, 06530 Ankara, Turkey","institution_ids":["https://openalex.org/I106245021"]},{"raw_affiliation_string":"Institute of Space Sciences, P.O. Box, MG-23, R 76900 Magurele-Bucharest, Romania","institution_ids":["https://openalex.org/I4210142834"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087794334","display_name":"Fairouz Tchier","orcid":"https://orcid.org/0000-0001-7855-508X"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fairouz Tchier","raw_affiliation_strings":["Department of Mathematics, King Saud University, P.O. BOX 2454, Riyadh 11451, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Saud University, P.O. BOX 2454, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016818633"],"corresponding_institution_ids":["https://openalex.org/I4210090124","https://openalex.org/I4210138655"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.8689,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.93917741,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"5","first_page":"384","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9987000226974487,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9975000023841858,"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/conformable-matrix","display_name":"Conformable matrix","score":0.9363890290260315},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7160258889198303},{"id":"https://openalex.org/keywords/sense","display_name":"Sense (electronics)","score":0.6957986950874329},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6834372282028198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5954521298408508},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4861714243888855},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.4533228278160095},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4406653046607971},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3949350118637085},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3352118730545044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.322115421295166},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21072903275489807},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19404619932174683},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08559682965278625},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08392968773841858},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.051385462284088135}],"concepts":[{"id":"https://openalex.org/C86072612","wikidata":"https://www.wikidata.org/wiki/Q5160239","display_name":"Conformable matrix","level":2,"score":0.9363890290260315},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7160258889198303},{"id":"https://openalex.org/C143141573","wikidata":"https://www.wikidata.org/wiki/Q7450971","display_name":"Sense (electronics)","level":2,"score":0.6957986950874329},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6834372282028198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5954521298408508},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4861714243888855},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.4533228278160095},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4406653046607971},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3949350118637085},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3352118730545044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.322115421295166},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21072903275489807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19404619932174683},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08559682965278625},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08392968773841858},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.051385462284088135},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e20050384","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20050384","pdf_url":"https://www.mdpi.com/1099-4300/20/5/384/pdf?version=1526807882","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33265474","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265474","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:mdpi.com:/1099-4300/20/5/384/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e20050384","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":"Entropy; Volume 20; Issue 5; Pages: 384","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7512903","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7512903","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e20050384","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20050384","pdf_url":"https://www.mdpi.com/1099-4300/20/5/384/pdf?version=1526807882","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"},{"id":"https://openalex.org/F4320335726","display_name":"Deanship of Scientific Research, King Saud University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2803524865.pdf","grobid_xml":"https://content.openalex.org/works/W2803524865.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W306873846","https://openalex.org/W1509146820","https://openalex.org/W1897068631","https://openalex.org/W1907528810","https://openalex.org/W1963489779","https://openalex.org/W1965360919","https://openalex.org/W1978349032","https://openalex.org/W1991089620","https://openalex.org/W2005520686","https://openalex.org/W2007463577","https://openalex.org/W2014725445","https://openalex.org/W2027955822","https://openalex.org/W2034392195","https://openalex.org/W2042099971","https://openalex.org/W2051063808","https://openalex.org/W2054709933","https://openalex.org/W2063067239","https://openalex.org/W2080931732","https://openalex.org/W2094551465","https://openalex.org/W2115419908","https://openalex.org/W2126272912","https://openalex.org/W2129268352","https://openalex.org/W2259227674","https://openalex.org/W2278954596","https://openalex.org/W2293755133","https://openalex.org/W2302503768","https://openalex.org/W2320344512","https://openalex.org/W2322303669","https://openalex.org/W2402496109","https://openalex.org/W2402673101","https://openalex.org/W2466188600","https://openalex.org/W2469685909","https://openalex.org/W2472805732","https://openalex.org/W2512232321","https://openalex.org/W2513888430","https://openalex.org/W2518297909","https://openalex.org/W2556784265","https://openalex.org/W2576606251","https://openalex.org/W2602740277","https://openalex.org/W2746834328","https://openalex.org/W2747750973","https://openalex.org/W2781864263","https://openalex.org/W2782439591","https://openalex.org/W2789619633","https://openalex.org/W2883573351","https://openalex.org/W2963641381","https://openalex.org/W3008849015","https://openalex.org/W3119407025","https://openalex.org/W4239707528","https://openalex.org/W4253062931","https://openalex.org/W4285719527","https://openalex.org/W6641004698","https://openalex.org/W6713169749","https://openalex.org/W6773950415","https://openalex.org/W6788487362"],"related_works":["https://openalex.org/W2792191619","https://openalex.org/W3158217983","https://openalex.org/W4248103533","https://openalex.org/W3046588275","https://openalex.org/W3085259849","https://openalex.org/W3046886605","https://openalex.org/W3008631921","https://openalex.org/W4313364931","https://openalex.org/W4302307873","https://openalex.org/W2898762024"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"a":[4],"numerical":[5,37,49],"simulation":[6],"of":[7,11,26,51,58,62,75],"fractional":[8,63],"conformable":[9,21,54,64],"attractors":[10,68],"type":[12,28,61],"Rabinovich-Fabrikant,":[13],"Thomas'":[14],"cyclically":[15],"symmetric":[16],"attractor":[17],"and":[18,22,65],"Newton-Leipnik.":[19],"Fractional":[20],"\u03b2":[23,66],"-conformable":[24,67],"derivatives":[25],"Liouville-Caputo":[27],"are":[29,69],"considered":[30],"to":[31,46,71],"solve":[32],"the":[33,41,48,52,59,73,76],"proposed":[34,77],"systems.":[35],"A":[36],"method":[38],"based":[39],"on":[40],"Adams-Moulton":[42],"algorithm":[43],"is":[44],"employed":[45],"approximate":[47],"simulations":[50],"fractional-order":[53],"attractors.":[55],"The":[56],"results":[57],"new":[60],"provided":[70],"illustrate":[72],"effectiveness":[74],"method.":[78]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}