{"id":"https://openalex.org/W2753321564","doi":"https://doi.org/10.1142/s0218127417501449","title":"A Technique for Studying a Class of Fractional-Order Nonlinear Dynamical Systems","display_name":"A Technique for Studying a Class of Fractional-Order Nonlinear Dynamical Systems","publication_year":2017,"publication_date":"2017-08-01","ids":{"openalex":"https://openalex.org/W2753321564","doi":"https://doi.org/10.1142/s0218127417501449","mag":"2753321564"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417501449","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501449","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030955773","display_name":"Gamal M. Mahmoud","orcid":"https://orcid.org/0000-0003-2673-8065"},"institutions":[{"id":"https://openalex.org/I91041137","display_name":"Assiut University","ror":"https://ror.org/01jaj8n65","country_code":"EG","type":"education","lineage":["https://openalex.org/I91041137"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Gamal M. Mahmoud","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt","institution_ids":["https://openalex.org/I91041137"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102965486","display_name":"Ahmed A. Farghaly","orcid":"https://orcid.org/0000-0002-9840-6986"},"institutions":[{"id":"https://openalex.org/I91041137","display_name":"Assiut University","ror":"https://ror.org/01jaj8n65","country_code":"EG","type":"education","lineage":["https://openalex.org/I91041137"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed A. M. Farghaly","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt","institution_ids":["https://openalex.org/I91041137"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076411196","display_name":"A.A.-H. Shoreh","orcid":"https://orcid.org/0000-0003-1982-0335"},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"A. A.-H. Shoreh","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt","institution_ids":["https://openalex.org/I184834183"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030955773"],"corresponding_institution_ids":["https://openalex.org/I91041137"],"apc_list":null,"apc_paid":null,"fwci":0.6162,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.66474847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"09","first_page":"1750144","last_page":"1750144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9969000220298767,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6522526741027832},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6082946062088013},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5675705671310425},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5547663569450378},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5532441139221191},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3770137131214142},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34654176235198975},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19399386644363403},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0987493097782135}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6522526741027832},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6082946062088013},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5675705671310425},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5547663569450378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5532441139221191},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3770137131214142},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34654176235198975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19399386644363403},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0987493097782135}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127417501449","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417501449","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1603797985","https://openalex.org/W1966553738","https://openalex.org/W1967763613","https://openalex.org/W1974932120","https://openalex.org/W1983396466","https://openalex.org/W2021684685","https://openalex.org/W2024556493","https://openalex.org/W2033932982","https://openalex.org/W2037545544","https://openalex.org/W2037876339","https://openalex.org/W2042461374","https://openalex.org/W2043086833","https://openalex.org/W2051022759","https://openalex.org/W2065126584","https://openalex.org/W2067577527","https://openalex.org/W2075664962","https://openalex.org/W2083410241","https://openalex.org/W2089031727","https://openalex.org/W2111108769","https://openalex.org/W2118244855","https://openalex.org/W2120827882","https://openalex.org/W2151015649","https://openalex.org/W2152254020","https://openalex.org/W2154953502","https://openalex.org/W2167203264","https://openalex.org/W2171637116","https://openalex.org/W2183087555","https://openalex.org/W2303324995","https://openalex.org/W2424414308","https://openalex.org/W2460663708","https://openalex.org/W2787959293","https://openalex.org/W4253062931","https://openalex.org/W4254873200","https://openalex.org/W4301223505"],"related_works":["https://openalex.org/W2000983461","https://openalex.org/W1985773265","https://openalex.org/W2164410746","https://openalex.org/W2070541395","https://openalex.org/W3196870860","https://openalex.org/W2052579244","https://openalex.org/W2001024694","https://openalex.org/W1965003407","https://openalex.org/W4312722051","https://openalex.org/W2783617944"],"abstract_inverted_index":{"In":[0],"this":[1,18,97],"work,":[2],"we":[3],"propose":[4],"a":[5],"technique":[6,19],"to":[7,21,27,90,126],"study":[8],"nonlinear":[9,48],"dynamical":[10,25,49,72],"systems":[11,38,85],"with":[12,69,81],"fractional-order.":[13],"The":[14],"main":[15],"idea":[16],"of":[17,96,105,123,131],"is":[20],"transform":[22],"the":[23,28,40,92,102,111,115,120,129,132,135],"fractional-order":[24,47,82,133],"system":[26,73,136],"integer":[29,70,121],"one":[30],"based":[31],"on":[32],"Jumarie\u2019s":[33],"modified":[34],"Riemann\u2013Liouville":[35],"sense.":[36],"Many":[37],"in":[39,79],"interdisciplinary":[41],"fields":[42],"could":[43],"be":[44,76],"described":[45],"by":[46],"systems,":[50,54],"such":[51],"as":[52,88],"viscoelastic":[53],"dielectric":[55],"polarization,":[56,58],"electrode-electrolyte":[57],"heat":[59],"conduction,":[60],"resistance-capacitance-inductance":[61],"(RLC)":[62],"interconnect":[63],"and":[64,94,109,113,134,141],"electromagnetic":[65],"waves.":[66],"To":[67],"deal":[68],"order":[71],"it":[74],"would":[75],"much":[77],"easier":[78],"contrast":[80],"system.":[83],"Two":[84],"are":[86],"considered":[87],"examples":[89,107],"illustrate":[91],"validity":[93],"advantages":[95],"technique.":[98],"We":[99,118],"have":[100],"calculated":[101],"Lyapunov":[103],"exponents":[104],"these":[106],"before":[108],"after":[110],"transformation":[112],"obtained":[114],"same":[116],"conclusions.":[117],"used":[119],"version":[122],"our":[124],"example":[125],"compute":[127],"numerically":[128],"values":[130],"parameters":[137],"at":[138],"which":[139],"chaotic":[140],"hyperchaotic":[142],"behaviors":[143],"exist.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}