{"id":"https://openalex.org/W4292575160","doi":"https://doi.org/10.3390/sym14081731","title":"Soliton Solutions and Sensitive Analysis of Modified Equal-Width Equation Using Fractional Operators","display_name":"Soliton Solutions and Sensitive Analysis of Modified Equal-Width Equation Using Fractional Operators","publication_year":2022,"publication_date":"2022-08-19","ids":{"openalex":"https://openalex.org/W4292575160","doi":"https://doi.org/10.3390/sym14081731"},"language":"en","primary_location":{"id":"doi:10.3390/sym14081731","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081731","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1731/pdf?version=1660893150","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/2073-8994/14/8/1731/pdf?version=1660893150","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101961190","display_name":"Muhammad Bilal Riaz","orcid":"https://orcid.org/0000-0001-5153-297X"},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]},{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK","PL"],"is_corresponding":true,"raw_author_name":"Muhammad Bilal Riaz","raw_affiliation_strings":["Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan","Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, 90-924 Lodz, Poland"],"raw_orcid":"https://orcid.org/0000-0001-5153-297X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan","institution_ids":["https://openalex.org/I87482320"]},{"raw_affiliation_string":"Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, 90-924 Lodz, Poland","institution_ids":["https://openalex.org/I188884621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076738654","display_name":"Adam Wojciechowski","orcid":"https://orcid.org/0000-0003-3786-7225"},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Adam Wojciechowski","raw_affiliation_strings":["Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, 90-924 Lodz, Poland"],"raw_orcid":"https://orcid.org/0000-0003-3786-7225","affiliations":[{"raw_affiliation_string":"Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, 90-924 Lodz, Poland","institution_ids":["https://openalex.org/I188884621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020913149","display_name":"Georgia Irina Oros","orcid":"https://orcid.org/0000-0003-2902-4455"},"institutions":[{"id":"https://openalex.org/I162871001","display_name":"University of Oradea","ror":"https://ror.org/00wzhv093","country_code":"RO","type":"education","lineage":["https://openalex.org/I162871001"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Georgia Irina Oros","raw_affiliation_strings":["Department of Mathematics and Computer Science, Univerisity of Oradea, 410087 Oradea, Romania"],"raw_orcid":"https://orcid.org/0000-0003-2902-4455","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Univerisity of Oradea, 410087 Oradea, Romania","institution_ids":["https://openalex.org/I162871001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114594068","display_name":"Riaz Ur Rahman","orcid":"https://orcid.org/0000-0001-9731-7212"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Riaz Ur Rahman","raw_affiliation_strings":["Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-9731-7212","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101961190"],"corresponding_institution_ids":["https://openalex.org/I188884621","https://openalex.org/I87482320"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.3763,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.89113402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"8","first_page":"1731","last_page":"1731"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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":0.9904999732971191,"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/soliton","display_name":"Soliton","score":0.6646215319633484},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5922300219535828},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5442587733268738},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5197427272796631},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5071990489959717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4850248694419861},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4565145969390869},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4478354752063751},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40267354249954224},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35000383853912354},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19832727313041687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11939767003059387},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10573926568031311}],"concepts":[{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.6646215319633484},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5922300219535828},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5442587733268738},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5197427272796631},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5071990489959717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4850248694419861},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4565145969390869},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4478354752063751},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40267354249954224},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35000383853912354},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19832727313041687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11939767003059387},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10573926568031311},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14081731","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081731","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1731/pdf?version=1660893150","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:addb8bea70bb4af0af282153e563488a","is_oa":true,"landing_page_url":"https://doaj.org/article/addb8bea70bb4af0af282153e563488a","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 8, p 1731 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/8/1731/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14081731","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14081731","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081731","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1731/pdf?version=1660893150","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":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4292575160.pdf"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W1994965507","https://openalex.org/W2006478547","https://openalex.org/W2025167479","https://openalex.org/W2038562396","https://openalex.org/W2044804236","https://openalex.org/W2087462514","https://openalex.org/W2094949990","https://openalex.org/W2116360589","https://openalex.org/W2161181790","https://openalex.org/W2213177993","https://openalex.org/W2267396220","https://openalex.org/W2267402960","https://openalex.org/W2402496109","https://openalex.org/W2733810313","https://openalex.org/W2799501512","https://openalex.org/W2883557885","https://openalex.org/W2896404797","https://openalex.org/W2905243872","https://openalex.org/W2919961923","https://openalex.org/W2922002939","https://openalex.org/W2963960857","https://openalex.org/W2965016096","https://openalex.org/W2985917132","https://openalex.org/W2996851671","https://openalex.org/W3006377786","https://openalex.org/W3024925239","https://openalex.org/W3115380054","https://openalex.org/W3155722045","https://openalex.org/W3158449552","https://openalex.org/W3159515351","https://openalex.org/W3172950100","https://openalex.org/W3173143397","https://openalex.org/W3186736272","https://openalex.org/W3195194291","https://openalex.org/W3196794271","https://openalex.org/W3198890464","https://openalex.org/W3202630770","https://openalex.org/W3210522918","https://openalex.org/W3217122413","https://openalex.org/W4200056505","https://openalex.org/W4200338174","https://openalex.org/W4205566267","https://openalex.org/W4210673211","https://openalex.org/W4221116238","https://openalex.org/W4223956051","https://openalex.org/W4224215934","https://openalex.org/W4225398577","https://openalex.org/W4280603200","https://openalex.org/W4281740790","https://openalex.org/W4282945173","https://openalex.org/W4287093332","https://openalex.org/W6649009660","https://openalex.org/W6651953647","https://openalex.org/W6656828133","https://openalex.org/W6672236902","https://openalex.org/W6677376599","https://openalex.org/W6804783693"],"related_works":["https://openalex.org/W4243145179","https://openalex.org/W2082446734","https://openalex.org/W4255875982","https://openalex.org/W4244853958","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W2029404707","https://openalex.org/W4285325679","https://openalex.org/W4246784705","https://openalex.org/W4231775656"],"abstract_inverted_index":{"In":[0,86,109],"this":[1],"manuscript,":[2],"the":[3,20,36,40,62,65,69,91,95,111,119,123,135,140,149],"novel":[4],"auxiliary":[5],"equation":[6],"methodology":[7],"(NAEM)":[8],"is":[9,58,98,115,125],"employed":[10,33],"to":[11,34,60,88,117,127],"scrutinize":[12],"various":[13],"forms":[14],"of":[15,39,64,83,107,148],"solitary":[16],"wave":[17,23],"solutions":[18,38,73,92],"for":[19,48],"modified":[21],"equal-width":[22],"(MEW)":[24],"equation.":[25],"M-truncated":[26],"along":[27],"with":[28],"Atangana\u2013Baleanu":[29],"(AB)-fractional":[30],"derivatives":[31],"are":[32,46],"study":[35,61],"soliton":[37,84],"problem.":[41],"The":[42],"fractional":[43,66],"MEW":[44],"equations":[45],"important":[47],"describing":[49],"hydro-magnetic":[50],"waves":[51],"in":[52,139],"cold":[53],"plasma.":[54],"A":[55],"comparative":[56],"analysis":[57],"utilized":[59],"influence":[63],"parameter":[67],"on":[68],"generated":[70],"solutions.":[71,85,108,121],"Secured":[72],"include":[74],"bright,":[75],"dark,":[76],"singular,":[77],"periodic":[78],"and":[79,102],"many":[80],"other":[81,89],"types":[82],"compared":[87],"methods,":[90],"demonstrate":[93],"that":[94,104],"proposed":[96],"technique":[97],"particularly":[99],"effective,":[100],"straightforward,":[101],"trustworthy":[103],"contains":[105],"families":[106],"addition,":[110],"symbolic":[112],"soft":[113],"computation":[114],"used":[116],"verify":[118],"obtained":[120],"Finally,":[122],"system":[124],"subjected":[126],"a":[128],"sensitive":[129],"analysis.":[130],"Integer-order":[131],"results":[132],"calculated":[133],"by":[134],"symmetry":[136],"method":[137],"present":[138,150],"literature":[141],"can":[142],"be":[143],"addressed":[144],"as":[145],"limiting":[146],"cases":[147],"study.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
