{"id":"https://openalex.org/W4410777490","doi":"https://doi.org/10.3390/axioms14060405","title":"Dynamical Systems with Fractional Derivatives: Focus on Phase Portraits and Plasma Wave Propagation Using Lakshmanan\u2013Porsezian\u2013Daniel Model","display_name":"Dynamical Systems with Fractional Derivatives: Focus on Phase Portraits and Plasma Wave Propagation Using Lakshmanan\u2013Porsezian\u2013Daniel Model","publication_year":2025,"publication_date":"2025-05-27","ids":{"openalex":"https://openalex.org/W4410777490","doi":"https://doi.org/10.3390/axioms14060405"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14060405","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060405","pdf_url":"https://www.mdpi.com/2075-1680/14/6/405/pdf?version=1748345735","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/2075-1680/14/6/405/pdf?version=1748345735","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072265427","display_name":"Ammad Hassan Khan","orcid":"https://orcid.org/0000-0003-0767-3032"},"institutions":[{"id":"https://openalex.org/I173207729","display_name":"University of Engineering and Technology Taxila","ror":"https://ror.org/03v00ka07","country_code":"PK","type":"education","lineage":["https://openalex.org/I173207729"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Abdul Ghaffar Khan","raw_affiliation_strings":["Department of Mathematical Sciences, University of Engineering and Technology, Taxila 47050, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Engineering and Technology, Taxila 47050, Pakistan","institution_ids":["https://openalex.org/I173207729"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060885426","display_name":"Muhammad Muddassar","orcid":"https://orcid.org/0000-0002-8433-1514"},"institutions":[{"id":"https://openalex.org/I173207729","display_name":"University of Engineering and Technology Taxila","ror":"https://ror.org/03v00ka07","country_code":"PK","type":"education","lineage":["https://openalex.org/I173207729"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Muddassar","raw_affiliation_strings":["Department of Mathematical Sciences, University of Engineering and Technology, Taxila 47050, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Engineering and Technology, Taxila 47050, Pakistan","institution_ids":["https://openalex.org/I173207729"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007426446","display_name":"Sultan Shoaib","orcid":"https://orcid.org/0000-0003-3937-5101"},"institutions":[{"id":"https://openalex.org/I179311214","display_name":"Gulf University for Science & Technology","ror":"https://ror.org/04d9rzd67","country_code":"KW","type":"education","lineage":["https://openalex.org/I179311214"]}],"countries":["KW"],"is_corresponding":true,"raw_author_name":"Sultan Shoaib","raw_affiliation_strings":["Department of Engineering, Gulf University of Science and Technology, Hawally 32093, Kuwait","GUST Engineering & Applied Innovation Research Centre (GEAR), Gulf University for Science and Technology, Hawally 32093, Kuwait"],"affiliations":[{"raw_affiliation_string":"Department of Engineering, Gulf University of Science and Technology, Hawally 32093, Kuwait","institution_ids":["https://openalex.org/I179311214"]},{"raw_affiliation_string":"GUST Engineering & Applied Innovation Research Centre (GEAR), Gulf University for Science and Technology, Hawally 32093, Kuwait","institution_ids":["https://openalex.org/I179311214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107547235","display_name":"Zia Ur Rehman","orcid":"https://orcid.org/0009-0009-0036-887X"},"institutions":[{"id":"https://openalex.org/I173207729","display_name":"University of Engineering and Technology Taxila","ror":"https://ror.org/03v00ka07","country_code":"PK","type":"education","lineage":["https://openalex.org/I173207729"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Zia Ur Rehman","raw_affiliation_strings":["Department of Mathematical Sciences, University of Engineering and Technology, Taxila 47050, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Engineering and Technology, Taxila 47050, Pakistan","institution_ids":["https://openalex.org/I173207729"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028930671","display_name":"Muhammad Zahid","orcid":"https://orcid.org/0000-0002-8613-2017"},"institutions":[{"id":"https://openalex.org/I173207729","display_name":"University of Engineering and Technology Taxila","ror":"https://ror.org/03v00ka07","country_code":"PK","type":"education","lineage":["https://openalex.org/I173207729"]},{"id":"https://openalex.org/I179311214","display_name":"Gulf University for Science & Technology","ror":"https://ror.org/04d9rzd67","country_code":"KW","type":"education","lineage":["https://openalex.org/I179311214"]}],"countries":["KW","PK"],"is_corresponding":true,"raw_author_name":"Muhammad Zahid","raw_affiliation_strings":["Department of Engineering, Gulf University of Science and Technology, Hawally 32093, Kuwait","Department of Telecommunication Engineering, University of Engineering and Technology, Taxila 47050, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Engineering, Gulf University of Science and Technology, Hawally 32093, Kuwait","institution_ids":["https://openalex.org/I179311214"]},{"raw_affiliation_string":"Department of Telecommunication Engineering, University of Engineering and Technology, Taxila 47050, Pakistan","institution_ids":["https://openalex.org/I173207729"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5007426446","https://openalex.org/A5028930671","https://openalex.org/A5107547235"],"corresponding_institution_ids":["https://openalex.org/I173207729","https://openalex.org/I179311214"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09426981,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"6","first_page":"405","last_page":"405"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"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/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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9994000196456909,"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/phase-portrait","display_name":"Phase portrait","score":0.786889910697937},{"id":"https://openalex.org/keywords/portrait","display_name":"Portrait","score":0.6108999252319336},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6057252287864685},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4697549641132355},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4216957986354828},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3824085295200348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3508947491645813},{"id":"https://openalex.org/keywords/history","display_name":"History","score":0.1001063883304596},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.09807020425796509},{"id":"https://openalex.org/keywords/art-history","display_name":"Art history","score":0.0897337794303894},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08747127652168274},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.08160755038261414}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.786889910697937},{"id":"https://openalex.org/C162462552","wikidata":"https://www.wikidata.org/wiki/Q134307","display_name":"Portrait","level":2,"score":0.6108999252319336},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6057252287864685},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4697549641132355},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4216957986354828},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3824085295200348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3508947491645813},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.1001063883304596},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.09807020425796509},{"id":"https://openalex.org/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.0897337794303894},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08747127652168274},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.08160755038261414},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14060405","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060405","pdf_url":"https://www.mdpi.com/2075-1680/14/6/405/pdf?version=1748345735","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:adb2f76c9afc4d269b1f1289ea21dc15","is_oa":true,"landing_page_url":"https://doaj.org/article/adb2f76c9afc4d269b1f1289ea21dc15","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 14, Iss 6, p 405 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14060405","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060405","pdf_url":"https://www.mdpi.com/2075-1680/14/6/405/pdf?version=1748345735","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410777490.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1223665043","https://openalex.org/W1994856744","https://openalex.org/W2036266090","https://openalex.org/W2053833421","https://openalex.org/W2088113453","https://openalex.org/W2121324809","https://openalex.org/W2237669391","https://openalex.org/W2617239842","https://openalex.org/W2991362353","https://openalex.org/W3005596600","https://openalex.org/W3048779905","https://openalex.org/W4224271958","https://openalex.org/W4254757986","https://openalex.org/W4292110664","https://openalex.org/W4312054340","https://openalex.org/W4313654679","https://openalex.org/W4380988288","https://openalex.org/W4386829326","https://openalex.org/W4388557326","https://openalex.org/W4390236378","https://openalex.org/W4391842452","https://openalex.org/W4399980439","https://openalex.org/W4401991357","https://openalex.org/W4402761236","https://openalex.org/W4403247763","https://openalex.org/W4404132286","https://openalex.org/W4404525035","https://openalex.org/W4404621365","https://openalex.org/W4407763282","https://openalex.org/W6874268156"],"related_works":["https://openalex.org/W2339458745","https://openalex.org/W2063032739","https://openalex.org/W2360001249","https://openalex.org/W594086971","https://openalex.org/W2315550989","https://openalex.org/W2031725242","https://openalex.org/W3169920643","https://openalex.org/W2141684174","https://openalex.org/W27177127","https://openalex.org/W1594354616"],"abstract_inverted_index":{"In":[0,165],"this":[1],"research,":[2],"we":[3,90,139],"investigate":[4],"the":[5,32,36,43,60,72,108,119,131,151,155,160,171,177,191,196,235,257],"phenomenon":[6],"of":[7,38,49,57,74,115,121,157,162,179,190,203,234,242,249],"multistability":[8],"and":[9,42,66,78,96,125,144,154,176,185,214,222,255,264],"complex":[10,113,152,180],"dynamic":[11],"behaviors":[12],"in":[13,59,84,149,252,261],"plasma":[14,27,61,85,136,163,253,262],"waves":[15,94,124],"by":[16,30,195],"utilizing":[17],"advanced":[18,270],"mathematical":[19],"techniques.":[20],"We":[21,117],"examine":[22],"how":[23,92],"fractional-order":[24],"derivatives":[25],"influence":[26],"wave":[28],"stability":[29,158,221],"applying":[31],"fractional":[33],"diffusion\u2013reaction":[34],"model,":[35],"framework":[37],"nonlinear":[39,198],"dynamical":[40,192],"systems,":[41,266],"(G\u2032G2)":[44],"method.":[45],"The":[46,188],"principal":[47],"direction":[48],"our":[50,167,247],"work":[51],"is":[52],"associated":[53],"with":[54],"different":[55,99,201],"forms":[56],"oscillations":[58,213],"wave:":[62],"non-linear":[63,142],"periodic,":[64],"solitons,":[65],"kink":[67,186],"waves.":[68,116,164,187],"This":[69],"leads":[70],"to":[71,129,147],"study":[73,118,168],"small":[75],"amplitude":[76],"pulses":[77],"solitary":[79],"waves,":[80],"which":[81,105],"are":[82],"significant":[83],"activities.":[86],"Using":[87],"bifurcation":[88],"analysis,":[89],"discuss":[91],"these":[93],"appear":[95],"develop":[97],"under":[98,225],"conditions,":[100],"as":[101,103,183,267,269],"well":[102,268],"determine":[104],"conditions":[106],"generate":[107,200],"chaotic":[109,127,250],"behavior":[110,128,251],"or":[111],"highly":[112],"patterns":[114,153,202,211],"details":[120],"transitions":[122],"between":[123,173],"their":[126,135],"characterize":[130],"laws":[132],"that":[133],"govern":[134],"environment.":[137],"Moreover,":[138],"have":[140],"used":[141],"modeling":[143],"numerical":[145],"simulations":[146],"understand":[148],"detail":[150],"factors":[156],"underlying":[159],"phenomena":[161],"addition,":[166],"also":[169],"investigates":[170],"correspondence":[172],"non-linearity,":[174],"multi-stability,":[175],"birth":[178],"structures":[181],"such":[182],"solitons":[184],"solutions":[189],"system":[193,207,220,243],"produced":[194],"proposed":[197,236],"model":[199],"response":[204],"based":[205],"on":[206],"parameter":[208,227],"variation.":[209],"These":[210],"include":[212],"decay":[215],"behaviors.":[216],"Research":[217],"results":[218],"about":[219],"solution":[223],"convergence":[224],"various":[226],"settings":[228],"provide":[229],"an":[230],"extended":[231],"performance":[232],"evaluation":[233],"method":[237],"through":[238],"a":[239],"better":[240],"understanding":[241,248],"dynamics.":[244],"They":[245],"increase":[246],"systems":[254],"pave":[256],"way":[258],"for":[259],"applications":[260],"physics":[263],"energy":[265],"technologies.":[271]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}