{"id":"https://openalex.org/W2104873285","doi":"https://doi.org/10.3233/jcm-140489","title":"Solving fractional Riccati differential equation based on operational matrices","display_name":"Solving fractional Riccati differential equation based on operational matrices","publication_year":2014,"publication_date":"2014-10-08","ids":{"openalex":"https://openalex.org/W2104873285","doi":"https://doi.org/10.3233/jcm-140489","mag":"2104873285"},"language":"en","primary_location":{"id":"doi:10.3233/jcm-140489","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jcm-140489","pdf_url":null,"source":{"id":"https://openalex.org/S2765058733","display_name":"Journal of Computational Methods in Sciences and Engineering","issn_l":"1472-7978","issn":["1472-7978","1875-8983"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Methods in Sciences and Engineering","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/A5043372865","display_name":"K. Krishnaveni","orcid":null},"institutions":[{"id":"https://openalex.org/I932239252","display_name":"SASTRA University","ror":"https://ror.org/032jk8892","country_code":"IN","type":"education","lineage":["https://openalex.org/I932239252"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"K. Krishnaveni","raw_affiliation_strings":["Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, Tamilnadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, Tamilnadu, India","institution_ids":["https://openalex.org/I932239252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026550770","display_name":"K. Kannan","orcid":"https://orcid.org/0000-0002-8837-3324"},"institutions":[{"id":"https://openalex.org/I932239252","display_name":"SASTRA University","ror":"https://ror.org/032jk8892","country_code":"IN","type":"education","lineage":["https://openalex.org/I932239252"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"K. Kannan","raw_affiliation_strings":["Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, Tamilnadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, Tamilnadu, India","institution_ids":["https://openalex.org/I932239252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102931104","display_name":"S. Raja Balachandar","orcid":null},"institutions":[{"id":"https://openalex.org/I932239252","display_name":"SASTRA University","ror":"https://ror.org/032jk8892","country_code":"IN","type":"education","lineage":["https://openalex.org/I932239252"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. Raja Balachandar","raw_affiliation_strings":["Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, Tamilnadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, Tamilnadu, India","institution_ids":["https://openalex.org/I932239252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I932239252"],"apc_list":null,"apc_paid":null,"fwci":0.2527,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60615555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"4-5","first_page":"229","last_page":"243"},"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":0.9945999979972839,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9916999936103821,"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/legendre-polynomials","display_name":"Legendre polynomials","score":0.8421527743339539},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.7081382870674133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6854212284088135},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.6573588848114014},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.607603132724762},{"id":"https://openalex.org/keywords/legendres-equation","display_name":"Legendre's equation","score":0.5724128484725952},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5652263164520264},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5543879866600037},{"id":"https://openalex.org/keywords/associated-legendre-polynomials","display_name":"Associated Legendre polynomials","score":0.5418624877929688},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.5303939580917358},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5190870761871338},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5177866220474243},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.49513259530067444},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3636627793312073},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.2814875841140747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14886167645454407},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.1325112283229828},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.09717857837677002}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8421527743339539},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.7081382870674133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6854212284088135},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.6573588848114014},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.607603132724762},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.5724128484725952},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5652263164520264},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5543879866600037},{"id":"https://openalex.org/C36956377","wikidata":"https://www.wikidata.org/wiki/Q228376","display_name":"Associated Legendre polynomials","level":5,"score":0.5418624877929688},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.5303939580917358},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5190870761871338},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5177866220474243},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.49513259530067444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3636627793312073},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.2814875841140747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14886167645454407},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.1325112283229828},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.09717857837677002},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jcm-140489","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jcm-140489","pdf_url":null,"source":{"id":"https://openalex.org/S2765058733","display_name":"Journal of Computational Methods in Sciences and Engineering","issn_l":"1472-7978","issn":["1472-7978","1875-8983"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Methods in Sciences and Engineering","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/W1517755115","https://openalex.org/W1522531528","https://openalex.org/W1582705120","https://openalex.org/W1597037182","https://openalex.org/W1964240999","https://openalex.org/W1969442376","https://openalex.org/W1970731741","https://openalex.org/W1975383112","https://openalex.org/W1975766919","https://openalex.org/W1985312627","https://openalex.org/W1994916853","https://openalex.org/W2002006488","https://openalex.org/W2011242297","https://openalex.org/W2012645543","https://openalex.org/W2013218122","https://openalex.org/W2015696140","https://openalex.org/W2017284163","https://openalex.org/W2019469368","https://openalex.org/W2022881593","https://openalex.org/W2025349820","https://openalex.org/W2056456131","https://openalex.org/W2061400438","https://openalex.org/W2061498519","https://openalex.org/W2067548886","https://openalex.org/W2078562191","https://openalex.org/W2079390764","https://openalex.org/W2084823492","https://openalex.org/W2086737859","https://openalex.org/W2091877690","https://openalex.org/W2103233901","https://openalex.org/W2134837756","https://openalex.org/W2152152827","https://openalex.org/W2170606157","https://openalex.org/W2787959293","https://openalex.org/W3000113561"],"related_works":["https://openalex.org/W1607269076","https://openalex.org/W2545227774","https://openalex.org/W2953361964","https://openalex.org/W3200178185","https://openalex.org/W3005861762","https://openalex.org/W4296546724","https://openalex.org/W2348706538","https://openalex.org/W2034418652","https://openalex.org/W2288349649","https://openalex.org/W1988418937"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,12,29],"solution":[4],"of":[5,15,23],"fractional":[6,31],"Riccati":[7],"differential":[8],"equation":[9],"by":[10],"using":[11],"operational":[13],"matrix":[14],"shifted":[16,24],"Legendre":[17,25],"polynomial":[18],"is":[19],"discussed.":[20],"The":[21],"properties":[22],"polynomials":[26],"together":[27],"with":[28],"Caputo":[30],"derivative":[32],"are":[33],"use":[34]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}