{"id":"https://openalex.org/W4309737137","doi":"https://doi.org/10.3390/axioms11110654","title":"Fractional Clique Collocation Technique for Numerical Simulations of Fractional-Order Brusselator Chemical Model","display_name":"Fractional Clique Collocation Technique for Numerical Simulations of Fractional-Order Brusselator Chemical Model","publication_year":2022,"publication_date":"2022-11-18","ids":{"openalex":"https://openalex.org/W4309737137","doi":"https://doi.org/10.3390/axioms11110654"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11110654","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110654","pdf_url":"https://www.mdpi.com/2075-1680/11/11/654/pdf?version=1670981839","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/11/654/pdf?version=1670981839","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023146926","display_name":"Mohammad Izadi","orcid":"https://orcid.org/0000-0002-6116-4928"},"institutions":[{"id":"https://openalex.org/I115566878","display_name":"Shahid Bahonar University of Kerman","ror":"https://ror.org/04zn42r77","country_code":"IR","type":"education","lineage":["https://openalex.org/I115566878"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Izadi","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran"],"raw_orcid":"https://orcid.org/0000-0002-6116-4928","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran","institution_ids":["https://openalex.org/I115566878"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079512627","display_name":"H. M. Srivastava","orcid":"https://orcid.org/0000-0002-9277-8092"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]},{"id":"https://openalex.org/I35928602","display_name":"Kyung Hee University","ror":"https://ror.org/01zqcg218","country_code":"KR","type":"education","lineage":["https://openalex.org/I35928602"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I87490745","display_name":"Azerbaijan University","ror":"https://ror.org/00g1psz15","country_code":"AZ","type":"education","lineage":["https://openalex.org/I87490745"]}],"countries":["AZ","CA","KR","TW"],"is_corresponding":true,"raw_author_name":"Hari Srivastava","raw_affiliation_strings":["Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea","Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan","Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-9277-8092","affiliations":[{"raw_affiliation_string":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea","institution_ids":["https://openalex.org/I35928602"]},{"raw_affiliation_string":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan","institution_ids":["https://openalex.org/I87490745"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5079512627"],"corresponding_institution_ids":["https://openalex.org/I184693016","https://openalex.org/I212119943","https://openalex.org/I35928602","https://openalex.org/I4210126829","https://openalex.org/I87490745"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":3.5847,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94253292,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"11","issue":"11","first_page":"654","last_page":"654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9757000207901001,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.97079998254776,"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/mathematics","display_name":"Mathematics","score":0.6007385849952698},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.578220009803772},{"id":"https://openalex.org/keywords/brusselator","display_name":"Brusselator","score":0.5749176144599915},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5659376978874207},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5154405832290649},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.45749813318252563},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.44043707847595215},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.418022096157074},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36058950424194336},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.32464176416397095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29225826263427734},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15151461958885193},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.14772292971611023}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6007385849952698},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.578220009803772},{"id":"https://openalex.org/C14028793","wikidata":"https://www.wikidata.org/wiki/Q906505","display_name":"Brusselator","level":3,"score":0.5749176144599915},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5659376978874207},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5154405832290649},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.45749813318252563},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.44043707847595215},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.418022096157074},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36058950424194336},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.32464176416397095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29225826263427734},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15151461958885193},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.14772292971611023},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms11110654","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110654","pdf_url":"https://www.mdpi.com/2075-1680/11/11/654/pdf?version=1670981839","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/15536","is_oa":true,"landing_page_url":"http://hdl.handle.net/1828/15536","pdf_url":"https://dspace.library.uvic.ca/bitstream/1828/15536/1/srivastava_harim_axioms_2022_FINAL.pdf","source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:8c91b2ebb2974db2a0bc19d8387e80c4","is_oa":true,"landing_page_url":"https://doaj.org/article/8c91b2ebb2974db2a0bc19d8387e80c4","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":"Axioms, Vol 11, Iss 11, p 654 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/11/654/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110654","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":"Axioms; Volume 11; Issue 11; Pages: 654","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11110654","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110654","pdf_url":"https://www.mdpi.com/2075-1680/11/11/654/pdf?version=1670981839","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4309737137.pdf","grobid_xml":"https://content.openalex.org/works/W4309737137.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W51404214","https://openalex.org/W433794350","https://openalex.org/W562378484","https://openalex.org/W1963942260","https://openalex.org/W1987251677","https://openalex.org/W1997980613","https://openalex.org/W2058139940","https://openalex.org/W2067896392","https://openalex.org/W2074150977","https://openalex.org/W2082864800","https://openalex.org/W2110657483","https://openalex.org/W2112841801","https://openalex.org/W2147869535","https://openalex.org/W2273665217","https://openalex.org/W2332569326","https://openalex.org/W2505203363","https://openalex.org/W2553162880","https://openalex.org/W2561098464","https://openalex.org/W2977539266","https://openalex.org/W3026568936","https://openalex.org/W3034511520","https://openalex.org/W3091839745","https://openalex.org/W3099850579","https://openalex.org/W3134387060","https://openalex.org/W3135883308","https://openalex.org/W3153636207","https://openalex.org/W3156837567","https://openalex.org/W3166501656","https://openalex.org/W3187829870","https://openalex.org/W3198172853","https://openalex.org/W3203282975","https://openalex.org/W3207529658","https://openalex.org/W3209768452","https://openalex.org/W4206326857","https://openalex.org/W4220957588","https://openalex.org/W4221098903","https://openalex.org/W4229030071","https://openalex.org/W4238188161","https://openalex.org/W4239670818","https://openalex.org/W4386643809","https://openalex.org/W6602103676","https://openalex.org/W6791462348","https://openalex.org/W6799087034","https://openalex.org/W6800954668","https://openalex.org/W6856666286"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2889856026","https://openalex.org/W2150070385","https://openalex.org/W2000247808","https://openalex.org/W2384941625"],"abstract_inverted_index":{"The":[0,38,48,69],"primary":[1],"focus":[2],"of":[3,11,21,24,26,33,46,55,72,90,110,133,147],"this":[4],"research":[5],"study":[6],"is":[7,41,76,93],"in":[8,30,43,95,119],"the":[9,31,44,53,56,60,73,80,105,111,120,125,131,142,148],"development":[10],"an":[12],"effective":[13],"hybrid":[14,74,150],"matrix":[15,151],"method":[16],"to":[17],"solve":[18],"a":[19,86,99],"class":[20],"nonlinear":[22,82],"systems":[23,84],"equations":[25],"fractional":[27,39],"order":[28],"arising":[29],"modeling":[32],"autocatalytic":[34],"chemical":[35],"reaction":[36],"problems.":[37],"operator":[40],"considered":[42],"sense":[45],"Liouville\u2013Caputo.":[47],"proposed":[49,112],"approach":[50,75],"relies":[51],"on":[52,65],"combination":[54],"quasi-linearization":[57],"technique":[58],"and":[59,107,145],"spectral":[61],"collocation":[62,152],"strategy":[63],"based":[64],"generalized":[66],"clique":[67],"bases.":[68],"main":[70],"feature":[71],"that":[77],"it":[78],"converts":[79],"governing":[81],"fractional-order":[83],"into":[85],"linear":[87],"algebraic":[88],"system":[89],"equations,":[91],"which":[92],"solved":[94],"each":[96],"iteration.":[97],"In":[98],"weighted":[100],"L2":[101],"norm,":[102],"we":[103,123],"prove":[104],"error":[106],"convergence":[108],"analysis":[109],"algorithm.":[113],"By":[114],"using":[115],"various":[116],"model":[117],"parameters":[118],"numerical":[121],"examples,":[122],"show":[124,141],"computational":[126],"efficacy":[127],"as":[128,130],"well":[129],"accuracy":[132,144],"our":[134],"approach.":[135],"Comparisons":[136],"with":[137],"existing":[138],"available":[139],"schemes":[140],"high":[143],"robustness":[146],"designed":[149],"technique.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":6}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}