{"id":"https://openalex.org/W3106795359","doi":"https://doi.org/10.3390/sym12121976","title":"Efficacious Analytical Technique Applied to Fractional Fornberg\u2013Whitham Model and Two-Dimensional Fractional Population Model","display_name":"Efficacious Analytical Technique Applied to Fractional Fornberg\u2013Whitham Model and Two-Dimensional Fractional Population Model","publication_year":2020,"publication_date":"2020-11-30","ids":{"openalex":"https://openalex.org/W3106795359","doi":"https://doi.org/10.3390/sym12121976","mag":"3106795359"},"language":"en","primary_location":{"id":"doi:10.3390/sym12121976","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121976","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1976/pdf","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/2073-8994/12/12/1976/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028288113","display_name":"Cyril Dennis Enyi","orcid":"https://orcid.org/0000-0001-9658-5864"},"institutions":[{"id":"https://openalex.org/I4210112337","display_name":"University of Hafr Al-Batin","ror":"https://ror.org/021jt1927","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210112337"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Cyril D. Enyi","raw_affiliation_strings":["Department of Mathematics, University of Hafr Al Batin, Hafar Al Batin 39524, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-9658-5864","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hafr Al Batin, Hafar Al Batin 39524, Saudi Arabia","institution_ids":["https://openalex.org/I4210112337"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028288113"],"corresponding_institution_ids":["https://openalex.org/I4210112337"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1052,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.51487105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"12","issue":"12","first_page":"1976","last_page":"1976"},"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":0.9952999949455261,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9624000191688538,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/fractional-calculus","display_name":"Fractional calculus","score":0.7207458019256592},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5387462377548218},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5365638136863708},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5137165784835815},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.5034629702568054},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.48418572545051575},{"id":"https://openalex.org/keywords/homotopy-perturbation-method","display_name":"Homotopy perturbation method","score":0.46930813789367676},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4614355266094208},{"id":"https://openalex.org/keywords/population-model","display_name":"Population model","score":0.41384586691856384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3345658779144287},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.2640678286552429},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1605614721775055},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08719900250434875},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0825251042842865}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7207458019256592},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5387462377548218},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5365638136863708},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5137165784835815},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.5034629702568054},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.48418572545051575},{"id":"https://openalex.org/C91328119","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy perturbation method","level":3,"score":0.46930813789367676},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4614355266094208},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.41384586691856384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3345658779144287},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.2640678286552429},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1605614721775055},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08719900250434875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0825251042842865},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12121976","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121976","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1976/pdf","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:b73bc972753d41e29654751a348beb1c","is_oa":true,"landing_page_url":"https://doaj.org/article/b73bc972753d41e29654751a348beb1c","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 12, Iss 12, p 1976 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/12/1976/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12121976","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/sym12121976","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121976","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1976/pdf","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":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W7148150","https://openalex.org/W80466079","https://openalex.org/W611121171","https://openalex.org/W634523187","https://openalex.org/W1972680854","https://openalex.org/W1994581379","https://openalex.org/W1998901158","https://openalex.org/W2001852106","https://openalex.org/W2027675706","https://openalex.org/W2036759408","https://openalex.org/W2036817185","https://openalex.org/W2056400535","https://openalex.org/W2057414857","https://openalex.org/W2069564733","https://openalex.org/W2073489703","https://openalex.org/W2078108630","https://openalex.org/W2119339119","https://openalex.org/W2134086237","https://openalex.org/W2159514670","https://openalex.org/W2187834687","https://openalex.org/W2285372851","https://openalex.org/W2322122565","https://openalex.org/W2328420499","https://openalex.org/W2509978510","https://openalex.org/W2551053413","https://openalex.org/W2566889043","https://openalex.org/W2603198540","https://openalex.org/W2611501776","https://openalex.org/W2754015846","https://openalex.org/W2773084900","https://openalex.org/W2787896416","https://openalex.org/W2802104762","https://openalex.org/W2887700535","https://openalex.org/W2888736971","https://openalex.org/W2910284919","https://openalex.org/W2913829066","https://openalex.org/W2921118750","https://openalex.org/W2938011410","https://openalex.org/W2940908222","https://openalex.org/W2947435667","https://openalex.org/W2950694106","https://openalex.org/W2952864763","https://openalex.org/W2954551212","https://openalex.org/W2970054927","https://openalex.org/W2971186194","https://openalex.org/W2973204085","https://openalex.org/W2980226101","https://openalex.org/W2982441300","https://openalex.org/W2986973281","https://openalex.org/W2990727463","https://openalex.org/W2994309626","https://openalex.org/W2995444071","https://openalex.org/W2999792156","https://openalex.org/W3002507058","https://openalex.org/W3031078889","https://openalex.org/W3034679539","https://openalex.org/W4236165936","https://openalex.org/W4243049761","https://openalex.org/W6603276773","https://openalex.org/W6664488561","https://openalex.org/W6683253041","https://openalex.org/W6695803124","https://openalex.org/W6700630823","https://openalex.org/W6725339327","https://openalex.org/W6766909617"],"related_works":["https://openalex.org/W2088506180","https://openalex.org/W2188605998","https://openalex.org/W2087729225","https://openalex.org/W2470744056","https://openalex.org/W1964997874","https://openalex.org/W1545358442","https://openalex.org/W4239956528","https://openalex.org/W1497843313","https://openalex.org/W2127579732","https://openalex.org/W2151283633"],"abstract_inverted_index":{"This":[0,15],"paper":[1],"presents":[2],"an":[3],"efficacious":[4],"analytical":[5,48],"and":[6,33,70,86],"numerical":[7],"method":[8],"for":[9],"solution":[10,49,57],"of":[11,46,62,80,95,103],"fractional":[12,30,36,67,73],"differential":[13],"equations.":[14],"technique,":[16],"here":[17],"in":[18],"named":[19],"q-HATM":[20,52,63,96,105],"(q-homotopy":[21],"analysis":[22,82,88],"transform":[23],"method)":[24],"is":[25],"applied":[26],"to":[27,64,91,112],"a":[28,34],"one-dimensional":[29],"Fornberg\u2013Whitham":[31,68],"model":[32,38,69],"two-dimensional":[35,72],"population":[37,74],"emanating":[39],"from":[40],"biological":[41],"sciences.":[42],"The":[43],"overwhelming":[44],"agreement":[45],"our":[47],"by":[50,78],"the":[51,55,60,66,71,93,104],"technique":[53,97],"with":[54],"exact":[56],"indeed":[58],"establishes":[59],"efficacy":[61],"solve":[65,113],"model.":[75],"Furthermore,":[76],"comparisons":[77],"means":[79],"extensive":[81],"using":[83,106],"numerics,":[84],"graphs":[85],"error":[87],"are":[89],"presented":[90],"affirm":[92],"preference":[94],"over":[98],"other":[99],"methods.":[100],"A":[101],"variant":[102],"symmetry":[107],"can":[108],"also":[109],"be":[110],"considered":[111],"these":[114],"problems.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}