{"id":"https://openalex.org/W4387342892","doi":"https://doi.org/10.3390/sym15101862","title":"Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes","display_name":"Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes","publication_year":2023,"publication_date":"2023-10-04","ids":{"openalex":"https://openalex.org/W4387342892","doi":"https://doi.org/10.3390/sym15101862"},"language":"en","primary_location":{"id":"doi:10.3390/sym15101862","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15101862","pdf_url":"https://www.mdpi.com/2073-8994/15/10/1862/pdf?version=1696412436","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/10/1862/pdf?version=1696412436","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041365912","display_name":"Asim Zafar","orcid":"https://orcid.org/0000-0003-2242-8529"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Asim Zafar","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61120, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-2242-8529","affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61120, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011614044","display_name":"Muhammad Raheel","orcid":"https://orcid.org/0000-0002-6088-1108"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Raheel","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61120, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61120, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100670258","display_name":"Mohamed R. Ali","orcid":"https://orcid.org/0000-0002-0795-0709"},"institutions":[{"id":"https://openalex.org/I186217134","display_name":"Future University in Egypt","ror":"https://ror.org/03s8c2x09","country_code":"EG","type":"education","lineage":["https://openalex.org/I186217134"]},{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mohamed R. Ali","raw_affiliation_strings":["Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha 13518, Egypt","Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha 13518, Egypt","institution_ids":["https://openalex.org/I207547235"]},{"raw_affiliation_string":"Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt","institution_ids":["https://openalex.org/I186217134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088076922","display_name":"\u0416\u0430\u0439\u0434\u0430\u0440\u044b \u041c\u044b\u0440\u0437\u0430\u043a\u0443\u043b\u043e\u0432\u0430","orcid":"https://orcid.org/0000-0002-4047-4484"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhaidary Myrzakulova","raw_affiliation_strings":["Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana 010000, Kazakhstan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana 010000, Kazakhstan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042426376","display_name":"Ahmet Bekir","orcid":"https://orcid.org/0000-0001-9394-4681"},"institutions":[{"id":"https://openalex.org/I4210091745","display_name":"Eski\u015fehir City Hospital","ror":"https://ror.org/00czdkn85","country_code":"TR","type":"healthcare","lineage":["https://openalex.org/I1303077703","https://openalex.org/I4210091745"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Ahmet Bekir","raw_affiliation_strings":["Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, Eskisehir 26030, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-9394-4681","affiliations":[{"raw_affiliation_string":"Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, Eskisehir 26030, Turkey","institution_ids":["https://openalex.org/I4210091745"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058341975","display_name":"Ratbay Myrzakulov","orcid":"https://orcid.org/0000-0002-5274-0815"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ratbay Myrzakulov","raw_affiliation_strings":["Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana 010000, Kazakhstan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana 010000, Kazakhstan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5042426376"],"corresponding_institution_ids":["https://openalex.org/I4210091745"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.2781,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.96216929,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"15","issue":"10","first_page":"1862","last_page":"1862"},"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":0.9973999857902527,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6069130301475525},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5386651754379272},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5316959619522095},{"id":"https://openalex.org/keywords/periodic-wave","display_name":"Periodic wave","score":0.5237272381782532},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5221291184425354},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.500084400177002},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.47209495306015015},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4521810710430145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4022522270679474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35676348209381104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35243138670921326},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3064020276069641},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.2532704174518585},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07417771220207214}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6069130301475525},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5386651754379272},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5316959619522095},{"id":"https://openalex.org/C2993172089","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Periodic wave","level":3,"score":0.5237272381782532},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5221291184425354},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.500084400177002},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.47209495306015015},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4521810710430145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4022522270679474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35676348209381104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35243138670921326},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3064020276069641},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.2532704174518585},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07417771220207214},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym15101862","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15101862","pdf_url":"https://www.mdpi.com/2073-8994/15/10/1862/pdf?version=1696412436","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6a72799c5066498eaf039149042ffba1","is_oa":false,"landing_page_url":"https://doaj.org/article/6a72799c5066498eaf039149042ffba1","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":"Symmetry, Vol 15, Iss 10, p 1862 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15101862","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15101862","pdf_url":"https://www.mdpi.com/2073-8994/15/10/1862/pdf?version=1696412436","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4387342892.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1995896722","https://openalex.org/W2004885044","https://openalex.org/W2051495326","https://openalex.org/W2055559698","https://openalex.org/W2079776520","https://openalex.org/W2555862172","https://openalex.org/W2765227907","https://openalex.org/W2769332788","https://openalex.org/W2770657736","https://openalex.org/W2773541801","https://openalex.org/W2894166497","https://openalex.org/W2913927477","https://openalex.org/W2942891028","https://openalex.org/W2955846448","https://openalex.org/W2963520255","https://openalex.org/W2969905104","https://openalex.org/W2997263932","https://openalex.org/W3017756524","https://openalex.org/W3095987984","https://openalex.org/W3118334588","https://openalex.org/W3122604834","https://openalex.org/W3133642390","https://openalex.org/W3156566230","https://openalex.org/W3183180624","https://openalex.org/W3195527294","https://openalex.org/W3200948649","https://openalex.org/W4220781147","https://openalex.org/W4224292164","https://openalex.org/W4280620858","https://openalex.org/W4283818607","https://openalex.org/W4293554971","https://openalex.org/W4362450364","https://openalex.org/W4363649902","https://openalex.org/W4384927005","https://openalex.org/W4385253004","https://openalex.org/W4385704422","https://openalex.org/W6663169203","https://openalex.org/W6789580918","https://openalex.org/W6794331329","https://openalex.org/W6844433889"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W1975289146","https://openalex.org/W4246784705","https://openalex.org/W3121927021","https://openalex.org/W2089892488","https://openalex.org/W2416906960","https://openalex.org/W2050580331","https://openalex.org/W3049300385"],"abstract_inverted_index":{"This":[0,23],"article":[1],"concerns":[2],"new":[3,18],"analytical":[4,129],"wave":[5,130],"solutions":[6,59,85,99,104,120,131],"of":[7,16,20,69,83,114,145,165],"the":[8,21,41,44,51,79,84,95,102,106,109,112,115,119,140,163,168],"Kuralay-II":[9],"equations":[10],"(K-IIAE":[11],"and":[12,35,50,66,75,91,148,181],"K-IIBE)":[13],"with":[14,88],"exploration":[15],"a":[17,146,150],"definition":[19],"derivative.":[22],"model":[24],"is":[25,121],"used":[26,172],"in":[27,105,167,173],"various":[28],"fields,":[29],"like":[30],"nonlinear":[31],"optics,":[32],"ferromagnetic":[33],"materials":[34],"optical":[36],"fibers.":[37],"For":[38,108],"this":[39,126,174],"purpose,":[40],"expa":[42],"function,":[43],"extended":[45],"sinh-Gordon":[46],"equation":[47],"expansion":[48],"scheme,":[49],"generalized":[52],"Kudryashov":[53],"schemes":[54,171],"were":[55],"utilized.":[56],"The":[57,98,128,155,170],"resulting":[58],"are":[60,73,86,132,176],"dark,":[61],"bright,":[62],"dark-bright,":[63],"periodic,":[64],"singular":[65],"other":[67,184],"kinds":[68],"solitons.":[70],"These":[71],"results":[72,156],"obtained":[74,100,157],"also":[76,122,159],"verified":[77],"by":[78],"Mathematica":[80,96],"tool.":[81,97],"Some":[82],"explained":[87],"2-D,":[89],"3-D":[90],"contour":[92],"plots":[93],"using":[94],"succede":[101],"present":[103],"literature.":[107],"first":[110],"time,":[111],"effect":[113],"fractional":[116,185],"derivative":[117],"on":[118],"shown":[123],"graphically":[124],"for":[125,152,162],"model.":[127],"highly":[133],"desirable":[134],"as":[135],"they":[136],"offer":[137],"insights":[138],"into":[139],"underlying":[141],"physics":[142],"or":[143],"mathematics":[144],"system":[147],"provide":[149],"framework":[151],"further":[153],"analysis.":[154],"can":[158],"be":[160],"fruitful":[161],"development":[164],"models":[166],"future.":[169],"research":[175],"effective,":[177],"easy":[178],"to":[179],"apply,":[180],"reliably":[182],"handle":[183],"non-linear":[186],"partial":[187],"differential":[188],"equations.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":18}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}