{"id":"https://openalex.org/W2990424252","doi":"https://doi.org/10.3390/sym11121431","title":"Application of Fractional Residual Power Series Algorithm to Solve Newell\u2013Whitehead\u2013Segel Equation of Fractional Order","display_name":"Application of Fractional Residual Power Series Algorithm to Solve Newell\u2013Whitehead\u2013Segel Equation of Fractional Order","publication_year":2019,"publication_date":"2019-11-20","ids":{"openalex":"https://openalex.org/W2990424252","doi":"https://doi.org/10.3390/sym11121431","mag":"2990424252"},"language":"en","primary_location":{"id":"doi:10.3390/sym11121431","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121431","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1431/pdf?version=1575352175","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/2073-8994/11/12/1431/pdf?version=1575352175","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025732055","display_name":"Rania Saadeh","orcid":"https://orcid.org/0000-0002-6394-1452"},"institutions":[{"id":"https://openalex.org/I153687341","display_name":"Zarqa University","ror":"https://ror.org/01wf1es90","country_code":"JO","type":"education","lineage":["https://openalex.org/I153687341"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Rania Saadeh","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan"],"raw_orcid":"https://orcid.org/0000-0002-6394-1452","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan","institution_ids":["https://openalex.org/I153687341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004534298","display_name":"Mohammad Alaroud","orcid":"https://orcid.org/0000-0001-9099-5619"},"institutions":[{"id":"https://openalex.org/I885383172","display_name":"National University of Malaysia","ror":"https://ror.org/00bw8d226","country_code":"MY","type":"education","lineage":["https://openalex.org/I885383172"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Mohammad Alaroud","raw_affiliation_strings":["Center for Modeling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor DE, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Modeling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor DE, Malaysia","institution_ids":["https://openalex.org/I885383172"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029673983","display_name":"Mohammed Al\u2010Smadi","orcid":"https://orcid.org/0000-0003-0226-7254"},"institutions":[{"id":"https://openalex.org/I33926330","display_name":"Al-Balqa Applied University","ror":"https://ror.org/00qedmt22","country_code":"JO","type":"education","lineage":["https://openalex.org/I33926330"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Mohammed Al-Smadi","raw_affiliation_strings":["Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan"],"raw_orcid":"https://orcid.org/0000-0003-0226-7254","affiliations":[{"raw_affiliation_string":"Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan","institution_ids":["https://openalex.org/I33926330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059989391","display_name":"Rokiah Rozita Ahmad","orcid":"https://orcid.org/0000-0002-1781-3716"},"institutions":[{"id":"https://openalex.org/I885383172","display_name":"National University of Malaysia","ror":"https://ror.org/00bw8d226","country_code":"MY","type":"education","lineage":["https://openalex.org/I885383172"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Rokiah Ahmad","raw_affiliation_strings":["Center for Modeling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor DE, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-1781-3716","affiliations":[{"raw_affiliation_string":"Center for Modeling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor DE, Malaysia","institution_ids":["https://openalex.org/I885383172"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108697696","display_name":"Ummul Salma Din","orcid":null},"institutions":[{"id":"https://openalex.org/I885383172","display_name":"National University of Malaysia","ror":"https://ror.org/00bw8d226","country_code":"MY","type":"education","lineage":["https://openalex.org/I885383172"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Ummul Salma Din","raw_affiliation_strings":["Center for Modeling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor DE, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Modeling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor DE, Malaysia","institution_ids":["https://openalex.org/I885383172"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059989391"],"corresponding_institution_ids":["https://openalex.org/I885383172"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.7628,"has_fulltext":true,"cited_by_count":48,"citation_normalized_percentile":{"value":0.90805687,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"11","issue":"12","first_page":"1431","last_page":"1431"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9556999802589417,"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"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.645660936832428},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6202998161315918},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6174795031547546},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.6136345863342285},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5648658275604248},{"id":"https://openalex.org/keywords/convergent-series","display_name":"Convergent series","score":0.5054864883422852},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47238969802856445},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4384097158908844},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3437961935997009},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3273290991783142},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13409423828125}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.645660936832428},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6202998161315918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6174795031547546},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.6136345863342285},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5648658275604248},{"id":"https://openalex.org/C1115519","wikidata":"https://www.wikidata.org/wiki/Q1211057","display_name":"Convergent series","level":3,"score":0.5054864883422852},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47238969802856445},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4384097158908844},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3437961935997009},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3273290991783142},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13409423828125},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11121431","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121431","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1431/pdf?version=1575352175","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:1a037ef144cb4383b804775df3a48e12","is_oa":true,"landing_page_url":"https://doaj.org/article/1a037ef144cb4383b804775df3a48e12","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 11, Iss 12, p 1431 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/12/1431/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11121431","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/sym11121431","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121431","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1431/pdf?version=1575352175","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":[{"id":"https://openalex.org/G3016819552","display_name":null,"funder_award_id":"GP-K007788 and GP-K006926","funder_id":"https://openalex.org/F4320322699","funder_display_name":"Universiti Kebangsaan Malaysia"}],"funders":[{"id":"https://openalex.org/F4320322699","display_name":"Universiti Kebangsaan Malaysia","ror":"https://ror.org/00bw8d226"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2990424252.pdf","grobid_xml":"https://content.openalex.org/works/W2990424252.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1850511188","https://openalex.org/W2059652518","https://openalex.org/W2165917005","https://openalex.org/W2344940833","https://openalex.org/W2414160073","https://openalex.org/W2519899354","https://openalex.org/W2605002585","https://openalex.org/W2744957862","https://openalex.org/W2789424404","https://openalex.org/W2809989124","https://openalex.org/W2811280868","https://openalex.org/W2892343378","https://openalex.org/W2897394303","https://openalex.org/W2901508580","https://openalex.org/W2913692467","https://openalex.org/W2915502985","https://openalex.org/W2920237743","https://openalex.org/W2937097319","https://openalex.org/W2954090117","https://openalex.org/W2956152145","https://openalex.org/W2974784212","https://openalex.org/W2976139966","https://openalex.org/W2979462596","https://openalex.org/W6665496195","https://openalex.org/W6752940364","https://openalex.org/W6755056496","https://openalex.org/W6768603507"],"related_works":["https://openalex.org/W4295136758","https://openalex.org/W4237434372","https://openalex.org/W27629369","https://openalex.org/W1993426457","https://openalex.org/W2372176563","https://openalex.org/W3023908574","https://openalex.org/W2068949639","https://openalex.org/W3023620486","https://openalex.org/W1767792260","https://openalex.org/W4254345474"],"abstract_inverted_index":{"The":[0,67],"Newell\u2013Whitehead\u2013Segel":[1,61],"equation":[2,62],"is":[3],"one":[4],"of":[5,19,63,84,126,161],"the":[6,17,44,60,64,78,82,106,121,127,135,138,145,149,155,159,162,170],"most":[7],"nonlinear":[8],"amplitude":[9],"equations":[10],"that":[11,88,153],"plays":[12],"a":[13,39,72,95,165],"significant":[14],"role":[15],"in":[16,24,54,94],"modeling":[18],"various":[20],"physical":[21],"phenomena":[22],"arising":[23],"fluid":[25],"mechanics,":[26],"solid-state":[27],"physics,":[28,31],"optics,":[29],"plasma":[30],"dispersion,":[32],"and":[33,81,124,131,140],"convection":[34],"system.":[35],"In":[36],"this":[37],"analysis,":[38],"recent":[40],"numeric-analytic":[41],"technique,":[42],"called":[43],"fractional":[45,65,97,156],"residual":[46],"power":[47,75,98],"series":[48,76,99],"(FRPS)":[49],"approach,":[50],"was":[51],"successfully":[52],"employed":[53],"obtaining":[55],"effective":[56],"approximate":[57,141],"solutions":[58],"to":[59,119,169],"sense.":[66],"proposed":[68,128,146],"algorithm":[69],"relies":[70],"on":[71],"generalized":[73],"classical":[74],"under":[77],"Caputo":[79],"sense":[80,167],"concept":[83],"an":[85,91],"error":[86],"function":[87],"systematically":[89],"produces":[90],"analytical":[92],"solution":[93,142,150,163],"convergent":[96],"form":[100],"with":[101,164],"accurately":[102],"computable":[103],"structures,":[104],"without":[105],"need":[107],"for":[108],"any":[109],"unphysical":[110],"restrictive":[111],"assumptions.":[112],"Meanwhile,":[113],"two":[114],"illustrative":[115],"applications":[116],"are":[117],"included":[118],"show":[120],"efficiency,":[122],"reliability,":[123],"performance":[125],"technique.":[129,147],"Plotted":[130],"numerical":[132],"results":[133],"indicated":[134],"compatibility":[136],"between":[137],"exact":[139],"obtained":[143],"by":[144],"Furthermore,":[148],"behavior":[151],"indicates":[152],"increasing":[154],"parameter":[157],"changes":[158],"nature":[160],"smooth":[166],"symmetrical":[168],"integer-order":[171],"state.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}