{"id":"https://openalex.org/W4396242573","doi":"https://doi.org/10.1016/j.camwa.2024.04.005","title":"A Chebyshev neural network-based numerical scheme to solve distributed-order fractional differential equations","display_name":"A Chebyshev neural network-based numerical scheme to solve distributed-order fractional differential equations","publication_year":2024,"publication_date":"2024-04-29","ids":{"openalex":"https://openalex.org/W4396242573","doi":"https://doi.org/10.1016/j.camwa.2024.04.005"},"language":"en","primary_location":{"id":"doi:10.1016/j.camwa.2024.04.005","doi":"https://doi.org/10.1016/j.camwa.2024.04.005","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2024.04.005","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; Mathematics with Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5012836779","display_name":"S M Sivalingam","orcid":"https://orcid.org/0000-0003-0818-9007","observed_orcids":["https://orcid.org/0000-0003-0818-9007"]},"institutions":[{"id":"https://openalex.org/I4400573194","display_name":"National Institute of Technology, Puducherry","ror":"https://ror.org/02tare285","country_code":"IN","type":"education","lineage":["https://openalex.org/I4400573194"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"S.M. Sivalingam","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India"],"raw_orcid":"https://orcid.org/0000-0003-0818-9007","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India","institution_ids":["https://openalex.org/I4400573194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031475130","display_name":"Pushpendra Kumar","orcid":"https://orcid.org/0000-0002-7755-2837","observed_orcids":["https://orcid.org/0000-0002-7755-2837"]},"institutions":[{"id":"https://openalex.org/I69050122","display_name":"Near East University","ror":"https://ror.org/02x8svs93","country_code":"CY","type":"education","lineage":["https://openalex.org/I69050122"]},{"id":"https://openalex.org/I96268669","display_name":"Okan University","ror":"https://ror.org/054d5vq03","country_code":"TR","type":"education","lineage":["https://openalex.org/I96268669"]}],"countries":["CY","TR"],"is_corresponding":false,"raw_author_name":"Pushpendra Kumar","raw_affiliation_strings":["Department of Mathematics, Mathematics Research Center, Near East University TRNC, Mersin 10, Turkey","Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-7755-2837","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mathematics Research Center, Near East University TRNC, Mersin 10, Turkey","institution_ids":["https://openalex.org/I69050122"]},{"raw_affiliation_string":"Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey","institution_ids":["https://openalex.org/I96268669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050728265","display_name":"Venkatesan Govindaraj","orcid":"https://orcid.org/0000-0002-6564-5358","observed_orcids":["https://orcid.org/0000-0002-6564-5358"]},"institutions":[{"id":"https://openalex.org/I4400573194","display_name":"National Institute of Technology, Puducherry","ror":"https://ror.org/02tare285","country_code":"IN","type":"education","lineage":["https://openalex.org/I4400573194"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"V. Govindaraj","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India","institution_ids":["https://openalex.org/I4400573194"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012836779"],"corresponding_institution_ids":["https://openalex.org/I4400573194"],"apc_list":{"value":3310,"currency":"USD","value_usd":3310},"apc_paid":null,"fwci":12.1002,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.99606581,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"164","issue":null,"first_page":"150","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.8086000084877014,"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":0.8086000084877014,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.12160000205039978,"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/T10320","display_name":"Neural Networks and Applications","score":0.011800000444054604,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chebyshev-neural-network","display_name":"Chebyshev neural network","score":0.9850000143051147},{"id":"https://openalex.org/keywords/extreme-learning-machine","display_name":"extreme learning machine","score":0.9319999814033508},{"id":"https://openalex.org/keywords/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.6200000047683716},{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.996999979019165},{"id":"https://openalex.org/keywords/numerical-solution-of-fractional-equations","display_name":"numerical solution of fractional equations","score":0.6949999928474426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8265868425369263},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6309047937393188},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.6112609505653381},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6030338406562805},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5837047100067139},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5369081497192383},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.5192099213600159},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5120647549629211},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.43302708864212036},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43065354228019714},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3850984573364258},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12128251791000366},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.camwa.2024.04.005","doi":"https://doi.org/10.1016/j.camwa.2024.04.005","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2024.04.005","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; Mathematics with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7114490205","display_name":null,"funder_award_id":"Ref.202122-TN13000109","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"},{"id":"https://openalex.org/G8098946064","display_name":null,"funder_award_id":"02011/18/2023 NBHM (R.P)/ R&D II/5952","funder_id":"https://openalex.org/F4320320768","funder_display_name":"Department of Atomic Energy, Government of India"}],"funders":[{"id":"https://openalex.org/F4320320767","display_name":"University Grants Commission","ror":"https://ror.org/04p800546"},{"id":"https://openalex.org/F4320320768","display_name":"Department of Atomic Energy, Government of India","ror":"https://ror.org/02m388s04"},{"id":"https://openalex.org/F4320323196","display_name":"National Board for Higher Mathematics","ror":"https://ror.org/02m388s04"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W1492972270","https://openalex.org/W1584611818","https://openalex.org/W1605182429","https://openalex.org/W1945981180","https://openalex.org/W1981340038","https://openalex.org/W2003360288","https://openalex.org/W2040329976","https://openalex.org/W2049106450","https://openalex.org/W2066229481","https://openalex.org/W2069610362","https://openalex.org/W2080793911","https://openalex.org/W2090239694","https://openalex.org/W2111072639","https://openalex.org/W2158985775","https://openalex.org/W2170888885","https://openalex.org/W2275233666","https://openalex.org/W2297274183","https://openalex.org/W2316109652","https://openalex.org/W2517020197","https://openalex.org/W2550887600","https://openalex.org/W2556784265","https://openalex.org/W2587375978","https://openalex.org/W2591074847","https://openalex.org/W2609290290","https://openalex.org/W2732497708","https://openalex.org/W2782302440","https://openalex.org/W2884204858","https://openalex.org/W2890443329","https://openalex.org/W2904185039","https://openalex.org/W2922646101","https://openalex.org/W2948851489","https://openalex.org/W2954075001","https://openalex.org/W3008525407","https://openalex.org/W3038970584","https://openalex.org/W3041411524","https://openalex.org/W3045233369","https://openalex.org/W3092432945","https://openalex.org/W3092489834","https://openalex.org/W3101766416","https://openalex.org/W3112199937","https://openalex.org/W3112440564","https://openalex.org/W3133604974","https://openalex.org/W3155529179","https://openalex.org/W3167190751","https://openalex.org/W3170003932","https://openalex.org/W3200175819","https://openalex.org/W3209704659","https://openalex.org/W4229452446","https://openalex.org/W4234512716","https://openalex.org/W4234913348","https://openalex.org/W4280647708","https://openalex.org/W4307211009","https://openalex.org/W4307288461","https://openalex.org/W4310980578","https://openalex.org/W4316469349","https://openalex.org/W4317666299","https://openalex.org/W4321617051","https://openalex.org/W4327590188","https://openalex.org/W4375858659","https://openalex.org/W4376648837","https://openalex.org/W4381051581","https://openalex.org/W4385776938","https://openalex.org/W4386708829","https://openalex.org/W4387046278"],"related_works":["https://openalex.org/W2595025956","https://openalex.org/W3085293658","https://openalex.org/W7132849056","https://openalex.org/W7130398785","https://openalex.org/W2550887600","https://openalex.org/W3045233369","https://openalex.org/W7112071988","https://openalex.org/W4411939960","https://openalex.org/W3216474391","https://openalex.org/W7170383018"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":16},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":9}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2024-04-30T00:00:00"}
