{"id":"https://openalex.org/W2789623424","doi":"https://doi.org/10.1080/00207160.2018.1438604","title":"Numerical solutions for systems of fractional order differential equations with Bernoulli wavelets","display_name":"Numerical solutions for systems of fractional order differential equations with Bernoulli wavelets","publication_year":2018,"publication_date":"2018-02-08","ids":{"openalex":"https://openalex.org/W2789623424","doi":"https://doi.org/10.1080/00207160.2018.1438604","mag":"2789623424"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2018.1438604","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1438604","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100444948","display_name":"Jiao Wang","orcid":"https://orcid.org/0000-0002-9011-6300"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiao Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108826552","display_name":"Tianzhou Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tian-Zhou Xu","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025262477","display_name":"Yan-Qiao Wei","orcid":"https://orcid.org/0000-0001-7620-3988"},"institutions":[{"id":"https://openalex.org/I12449238","display_name":"Universit\u00e9 d'Orl\u00e9ans","ror":"https://ror.org/014zrew76","country_code":"FR","type":"education","lineage":["https://openalex.org/I12449238"]},{"id":"https://openalex.org/I4210129154","display_name":"Centre Val de Loire","ror":"https://ror.org/03ntmtb29","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210088668","https://openalex.org/I4210129154"]},{"id":"https://openalex.org/I4210143826","display_name":"Institut National des Sciences Appliqu\u00e9es Centre Val de Loire","ror":"https://ror.org/03y0qc033","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210143826"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Yan-Qiao Wei","raw_affiliation_strings":["INSA Centre Val de Loire, Universit\u00e9 d'Orl\u00e9ans, Bourges Cedex, France"],"affiliations":[{"raw_affiliation_string":"INSA Centre Val de Loire, Universit\u00e9 d'Orl\u00e9ans, Bourges Cedex, France","institution_ids":["https://openalex.org/I4210143826","https://openalex.org/I4210129154","https://openalex.org/I12449238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088913520","display_name":"Jiaquan Xie","orcid":"https://orcid.org/0000-0002-1323-5402"},"institutions":[{"id":"https://openalex.org/I46305995","display_name":"Taiyuan University of Science and Technology","ror":"https://ror.org/01wcbdc92","country_code":"CN","type":"education","lineage":["https://openalex.org/I46305995"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia-Quan Xie","raw_affiliation_strings":["College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, People's Republic of China","institution_ids":["https://openalex.org/I46305995"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100444948"],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":1.6009,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.82328337,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"96","issue":"2","first_page":"317","last_page":"336"},"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/T11081","display_name":"Advanced Control Systems Design","score":0.9923999905586243,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.991100013256073,"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":0.8104166388511658},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.6068984866142273},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5792086720466614},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.5737614035606384},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47403573989868164},{"id":"https://openalex.org/keywords/bernoulli-polynomials","display_name":"Bernoulli polynomials","score":0.4728831648826599},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4611073136329651},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.44150394201278687},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4379636347293854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4146007001399994},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4129057824611664},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.10980537533760071},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10872888565063477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08279788494110107}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8104166388511658},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.6068984866142273},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5792086720466614},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5737614035606384},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47403573989868164},{"id":"https://openalex.org/C196172290","wikidata":"https://www.wikidata.org/wiki/Q2346201","display_name":"Bernoulli polynomials","level":4,"score":0.4728831648826599},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4611073136329651},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.44150394201278687},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4379636347293854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4146007001399994},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4129057824611664},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.10980537533760071},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10872888565063477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08279788494110107},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2018.1438604","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1438604","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W827447899","https://openalex.org/W1509146820","https://openalex.org/W1969308726","https://openalex.org/W1978367627","https://openalex.org/W1988892282","https://openalex.org/W2000737269","https://openalex.org/W2002386912","https://openalex.org/W2004531333","https://openalex.org/W2005421374","https://openalex.org/W2017705708","https://openalex.org/W2019469368","https://openalex.org/W2026220600","https://openalex.org/W2028721029","https://openalex.org/W2037545544","https://openalex.org/W2040722980","https://openalex.org/W2046459700","https://openalex.org/W2051849157","https://openalex.org/W2065898229","https://openalex.org/W2067622555","https://openalex.org/W2076575482","https://openalex.org/W2080059419","https://openalex.org/W2084814282","https://openalex.org/W2086782152","https://openalex.org/W2087034446","https://openalex.org/W2094012975","https://openalex.org/W2149522752","https://openalex.org/W2151015649","https://openalex.org/W2160045938","https://openalex.org/W2202473431","https://openalex.org/W2215249091","https://openalex.org/W2319089385","https://openalex.org/W2336178288","https://openalex.org/W2399938728","https://openalex.org/W2613444522","https://openalex.org/W4253062931"],"related_works":["https://openalex.org/W3149859510","https://openalex.org/W2378928947","https://openalex.org/W2077222120","https://openalex.org/W3110769337","https://openalex.org/W2028074687","https://openalex.org/W3046757444","https://openalex.org/W2911908715","https://openalex.org/W2070850668","https://openalex.org/W3151534546","https://openalex.org/W3153101194"],"abstract_inverted_index":{"In":[0],"this":[1,39],"paper,":[2],"an":[3],"effective":[4],"algorithm":[5,18,40,80],"for":[6,31],"solving":[7],"systems":[8,32,58,66],"of":[9,33,38,59,67,78,84],"fractional":[10,50,60],"order":[11],"differential":[12,61],"equations":[13,62],"(FDEs)":[14],"is":[15,19,41],"proposed.":[16],"The":[17,35],"based":[20],"on":[21],"Bernoulli":[22,44],"wavelets":[23,45],"function":[24,46],"approximation,":[25],"which":[26],"has":[27],"never":[28],"been":[29],"used":[30],"FDEs.":[34],"main":[36],"purpose":[37],"to":[42,54,74],"combine":[43],"approximation":[47],"with":[48],"its":[49],"integral":[51],"operator":[52],"matrix":[53],"transform":[55],"the":[56,76,79,82,85],"studied":[57],"into":[63],"easily":[64],"solved":[65],"algebraic":[68],"equations.":[69],"Illustrative":[70],"examples":[71],"are":[72],"included":[73],"reveal":[75],"effectiveness":[77],"and":[81],"accuracy":[83],"convergence":[86],"analysis.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2025-10-10T00:00:00"}
