{"id":"https://openalex.org/W4297860460","doi":"https://doi.org/10.3390/sym14091944","title":"Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series","display_name":"Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series","publication_year":2022,"publication_date":"2022-09-18","ids":{"openalex":"https://openalex.org/W4297860460","doi":"https://doi.org/10.3390/sym14091944"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091944","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091944","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1944/pdf?version=1663814454","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/2073-8994/14/9/1944/pdf?version=1663814454","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036773664","display_name":"A. A. Alderremy","orcid":"https://orcid.org/0000-0002-7401-0522"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Aisha Abdullah Alderremy","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083354054","display_name":"Rasool Shah","orcid":"https://orcid.org/0000-0003-4306-8489"},"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":"Rasool Shah","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University, Mardan P.O. Box 1100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-4306-8489","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University, Mardan P.O. Box 1100, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081449036","display_name":"Naveed Iqbal","orcid":"https://orcid.org/0000-0002-8548-7078"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Naveed Iqbal","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il P.O. Box 2440, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il P.O. Box 2440, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-8548-7078","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il P.O. Box 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il P.O. Box 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072394306","display_name":"Shaban Aly","orcid":null},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Shaban Aly","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, AL-Azhar University, Assiut 71516, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-8286-8123","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, AL-Azhar University, Assiut 71516, Egypt","institution_ids":["https://openalex.org/I184834183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089496116","display_name":"Kamsing Nonlaopon","orcid":"https://orcid.org/0000-0002-7469-5402"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Kamsing Nonlaopon","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-7469-5402","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5089496116"],"corresponding_institution_ids":["https://openalex.org/I179193067"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":9.7724,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.99235282,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"14","issue":"9","first_page":"1944","last_page":"1944"},"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":0.9900000095367432,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9891999959945679,"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/brusselator","display_name":"Brusselator","score":0.867477536201477},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7404356002807617},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.7247254848480225},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.7104827165603638},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6968281865119934},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6756258010864258},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6016746759414673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5690567493438721},{"id":"https://openalex.org/keywords/convergent-series","display_name":"Convergent series","score":0.4863596558570862},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.44658592343330383},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.425983190536499},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28345221281051636},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1970788538455963},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06699308753013611}],"concepts":[{"id":"https://openalex.org/C14028793","wikidata":"https://www.wikidata.org/wiki/Q906505","display_name":"Brusselator","level":3,"score":0.867477536201477},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7404356002807617},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.7247254848480225},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.7104827165603638},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6968281865119934},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6756258010864258},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6016746759414673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5690567493438721},{"id":"https://openalex.org/C1115519","wikidata":"https://www.wikidata.org/wiki/Q1211057","display_name":"Convergent series","level":3,"score":0.4863596558570862},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.44658592343330383},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.425983190536499},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28345221281051636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1970788538455963},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06699308753013611},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14091944","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091944","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1944/pdf?version=1663814454","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:820fb707114b4b34bc408cab24a39c35","is_oa":true,"landing_page_url":"https://doaj.org/article/820fb707114b4b34bc408cab24a39c35","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 9, p 1944 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1944/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091944","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/sym14091944","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091944","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1944/pdf?version=1663814454","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/W4297860460.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W2009447804","https://openalex.org/W2066336292","https://openalex.org/W2170182000","https://openalex.org/W2338392580","https://openalex.org/W2499396687","https://openalex.org/W2922428687","https://openalex.org/W2956731362","https://openalex.org/W2962923242","https://openalex.org/W2969712265","https://openalex.org/W3007381669","https://openalex.org/W3028302063","https://openalex.org/W3029070471","https://openalex.org/W3034548093","https://openalex.org/W3034766284","https://openalex.org/W3042974430","https://openalex.org/W3108382869","https://openalex.org/W3129949328","https://openalex.org/W3137921994","https://openalex.org/W3181660949","https://openalex.org/W3190788454","https://openalex.org/W3200640456","https://openalex.org/W4210413586","https://openalex.org/W4221026216","https://openalex.org/W4221031129","https://openalex.org/W4221102633","https://openalex.org/W4225590972","https://openalex.org/W4226018711","https://openalex.org/W4226354586","https://openalex.org/W4231069456","https://openalex.org/W4236165936","https://openalex.org/W4253399077","https://openalex.org/W4256340197","https://openalex.org/W4280490815","https://openalex.org/W4280501108","https://openalex.org/W4281892403","https://openalex.org/W4285009971","https://openalex.org/W4291520297","https://openalex.org/W6666805008","https://openalex.org/W6703585480","https://openalex.org/W6724267018","https://openalex.org/W6809462662"],"related_works":["https://openalex.org/W4317627639","https://openalex.org/W4313396013","https://openalex.org/W3024206168","https://openalex.org/W3005643231","https://openalex.org/W2806181810","https://openalex.org/W3049179502","https://openalex.org/W1657036994","https://openalex.org/W2944128024","https://openalex.org/W3099844082","https://openalex.org/W2560757601"],"abstract_inverted_index":{"This":[0],"article":[1],"investigates":[2],"different":[3],"nonlinear":[4,105],"systems":[5],"of":[6,29,54,85],"fractional":[7],"partial":[8],"differential":[9],"equations":[10],"analytically":[11],"using":[12],"an":[13],"attractive":[14],"modified":[15],"method":[16,92],"known":[17],"as":[18],"the":[19,30,34,52,55,63,76,86,91,102],"Laplace":[20,31],"residual":[21,35,64],"power":[22,36,65],"series":[23,37,48,66],"technique.":[24],"Based":[25],"on":[26],"a":[27],"combination":[28],"transformation":[32],"and":[33,42,60,72,81,98],"technique,":[38],"we":[39],"achieve":[40],"analytic":[41],"approximation":[43],"results":[44],"in":[45],"rapid":[46],"convergent":[47],"form":[49],"by":[50],"employing":[51],"notion":[53],"limit,":[56],"with":[57],"less":[58],"time":[59],"effort":[61],"than":[62],"method.":[67],"Three":[68],"challenges":[69],"are":[70],"evaluated":[71],"simulated":[73],"to":[74,104],"validate":[75],"suggested":[77],"method\u2019s":[78],"practicability,":[79],"efficiency,":[80],"simplicity.":[82],"The":[83],"analysis":[84],"acquired":[87],"findings":[88],"demonstrates":[89],"that":[90],"mentioned":[93],"above":[94],"is":[95],"simple,":[96],"accurate,":[97],"appropriate":[99],"for":[100],"investigating":[101],"solutions":[103],"applied":[106],"sciences":[107],"models.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":29},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":4}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2025-10-10T00:00:00"}
