{"id":"https://openalex.org/W2996639562","doi":"https://doi.org/10.1155/2019/1741958","title":"Optimum Solutions of Fractional Order Zakharov\u2013Kuznetsov Equations","display_name":"Optimum Solutions of Fractional Order Zakharov\u2013Kuznetsov Equations","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2996639562","doi":"https://doi.org/10.1155/2019/1741958","mag":"2996639562"},"language":"en","primary_location":{"id":"doi:10.1155/2019/1741958","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/1741958","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/1741958.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/1741958.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063807836","display_name":"Rashid Nawaz","orcid":"https://orcid.org/0000-0002-4773-8446"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rashid Nawaz","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khaber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khaber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067688087","display_name":"Laiq Zada","orcid":null},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Laiq Zada","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khaber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khaber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035434177","display_name":"Abraiz Khattak","orcid":"https://orcid.org/0000-0003-1433-8304"},"institutions":[{"id":"https://openalex.org/I4210095908","display_name":"Advanced Energy (United States)","ror":"https://ror.org/00rs9dy63","country_code":"US","type":"company","lineage":["https://openalex.org/I4210095908"]},{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK","US"],"is_corresponding":false,"raw_author_name":"Abraiz Khattak","raw_affiliation_strings":["Department of Electrical Power Engineering, U.S. Pakistan Center for Advanced Studies in Energy,","National University of Sciences and Technology (NUST), Islamabad, Pakistan","Department of Electrical Power Engineering, U.S. Pakistan Center for Advanced Studies in Energy, National University of Sciences and Technology (NUST), Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Power Engineering, U.S. Pakistan Center for Advanced Studies in Energy,","institution_ids":["https://openalex.org/I4210095908"]},{"raw_affiliation_string":"National University of Sciences and Technology (NUST), Islamabad, Pakistan","institution_ids":["https://openalex.org/I929597975"]},{"raw_affiliation_string":"Department of Electrical Power Engineering, U.S. Pakistan Center for Advanced Studies in Energy, National University of Sciences and Technology (NUST), Islamabad, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070779330","display_name":"Muhammad Jibran","orcid":null},"institutions":[{"id":"https://openalex.org/I202376891","display_name":"Sarhad University of Science and Information Technology","ror":"https://ror.org/04dx2y384","country_code":"PK","type":"education","lineage":["https://openalex.org/I202376891"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Jibran","raw_affiliation_strings":["Department of Computer Science and IT, Sarhad University of Science and Information Technology, Peshawar, Khaber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and IT, Sarhad University of Science and Information Technology, Peshawar, Khaber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I202376891"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101514014","display_name":"Adam Khan","orcid":"https://orcid.org/0000-0001-6490-8809"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Adam Khan","raw_affiliation_strings":["Department for Management of Science and Technology Development, Ton Duc ang University, Ho Chi Minh City, Vietnam","Faculty of Electrical & Electronics Engineering, Ton Duc ang University, Ho Chi Minh City, Vietnam","Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam","Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department for Management of Science and Technology Development, Ton Duc ang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Faculty of Electrical & Electronics Engineering, Ton Duc ang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101514014"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.9231,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.85723077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9987999796867371,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6960323452949524},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5910293459892273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5366024374961853},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0966726541519165}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6960323452949524},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5910293459892273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5366024374961853},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0966726541519165},{"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:10.1155/2019/1741958","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/1741958","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/1741958.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:1741958","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/1741958.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:e558f61c2f9740aead60dad8d371b918","is_oa":true,"landing_page_url":"https://doaj.org/article/e558f61c2f9740aead60dad8d371b918","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/1741958","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/1741958","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/1741958.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322802","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2996639562.pdf","grobid_xml":"https://content.openalex.org/works/W2996639562.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W912616841","https://openalex.org/W1923079366","https://openalex.org/W1966675876","https://openalex.org/W1969421993","https://openalex.org/W1972478479","https://openalex.org/W1973950856","https://openalex.org/W1977360274","https://openalex.org/W1992828457","https://openalex.org/W1993445800","https://openalex.org/W2018598574","https://openalex.org/W2019469368","https://openalex.org/W2031523249","https://openalex.org/W2033598679","https://openalex.org/W2034662763","https://openalex.org/W2043909628","https://openalex.org/W2059348829","https://openalex.org/W2060124122","https://openalex.org/W2063222758","https://openalex.org/W2065261142","https://openalex.org/W2070454382","https://openalex.org/W2091474129","https://openalex.org/W2097982718","https://openalex.org/W2126825471","https://openalex.org/W2134603324","https://openalex.org/W2142758723","https://openalex.org/W2170606157","https://openalex.org/W2295645578","https://openalex.org/W2314482512","https://openalex.org/W2402750567","https://openalex.org/W2561675875","https://openalex.org/W2609272154","https://openalex.org/W2742053859","https://openalex.org/W2752563468","https://openalex.org/W2787959293","https://openalex.org/W2792655170","https://openalex.org/W2921893094","https://openalex.org/W2943078437","https://openalex.org/W2964461289","https://openalex.org/W3106152561"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,12,34,41,47,52,66,77,84],"Optimal":[4],"Homotopy":[5],"Asymptotic":[6],"Method":[7],"is":[8,27,69,86],"extended":[9],"to":[10],"derive":[11],"approximate":[13],"solutions":[14,45],"of":[15,46,54,65,92,94],"fractional":[16,23,36,96],"order":[17,24,97],"two\u2010dimensional":[18],"partial":[19,98],"differential":[20,99],"equations.":[21,100],"The":[22,44,79],"Zakharov\u2013Kuznetsov":[25],"equation":[26],"solved":[28],"as":[29],"a":[30],"test":[31],"example,":[32],"while":[33],"time":[35],"derivatives":[37],"are":[38,49],"described":[39],"in":[40,51,76],"Caputo":[42],"sense.":[43],"problem":[48],"computed":[50],"form":[53],"rapidly":[55],"convergent":[56],"series":[57],"with":[58,73],"easily":[59],"calculable":[60],"components":[61],"using":[62],"Mathematica.":[63],"Reliability":[64],"proposed":[67],"method":[68,85],"given":[70],"by":[71],"comparison":[72],"other":[74],"methods":[75],"literature.":[78],"obtained":[80],"results":[81],"showed":[82],"that":[83],"powerful":[87],"and":[88],"efficient":[89],"for":[90],"determination":[91],"solution":[93],"higher\u2010dimensional":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}