{"id":"https://openalex.org/W3169710284","doi":"https://doi.org/10.1007/s12190-021-01573-2","title":"A minimal search method for solving fractional integro-differential equations based on modified Legendre multiwavelets","display_name":"A minimal search method for solving fractional integro-differential equations based on modified Legendre multiwavelets","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3169710284","doi":"https://doi.org/10.1007/s12190-021-01573-2","mag":"3169710284"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-021-01573-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-021-01573-2","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","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/A5023561022","display_name":"Longbin Wu","orcid":"https://orcid.org/0000-0003-1290-9564"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longbin Wu","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101839453","display_name":"Zhong Chen","orcid":"https://orcid.org/0000-0001-8013-9798"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhong Chen","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101413900","display_name":"Xiaohua Ding","orcid":"https://orcid.org/0000-0002-0983-3522"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaohua Ding","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101413900"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.3377,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.52141581,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"68","issue":"2","first_page":"1467","last_page":"1483"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/legendre-polynomials","display_name":"Legendre polynomials","score":0.8429274559020996},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8346887826919556},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.6248356103897095},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5603311061859131},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.535883367061615},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4894927740097046},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4857824146747589},{"id":"https://openalex.org/keywords/legendres-equation","display_name":"Legendre's equation","score":0.4566586911678314},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4465300738811493},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4351329803466797},{"id":"https://openalex.org/keywords/sinc-function","display_name":"Sinc function","score":0.4229796230792999},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.3941287696361542},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18747848272323608},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.17087867856025696},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1334177553653717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09912264347076416},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.09641271829605103}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8429274559020996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8346887826919556},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.6248356103897095},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5603311061859131},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.535883367061615},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4894927740097046},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4857824146747589},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.4566586911678314},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4465300738811493},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4351329803466797},{"id":"https://openalex.org/C152303783","wikidata":"https://www.wikidata.org/wiki/Q855949","display_name":"Sinc function","level":2,"score":0.4229796230792999},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.3941287696361542},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18747848272323608},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.17087867856025696},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1334177553653717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09912264347076416},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.09641271829605103},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12190-021-01573-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-021-01573-2","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2171199778","display_name":null,"funder_award_id":"ZR2020MA050","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W193812311","https://openalex.org/W563777065","https://openalex.org/W578475266","https://openalex.org/W600139552","https://openalex.org/W1545761024","https://openalex.org/W1967569646","https://openalex.org/W1975670568","https://openalex.org/W1985438383","https://openalex.org/W2011660400","https://openalex.org/W2024842502","https://openalex.org/W2039993822","https://openalex.org/W2047450993","https://openalex.org/W2057303584","https://openalex.org/W2058191269","https://openalex.org/W2064216226","https://openalex.org/W2073374589","https://openalex.org/W2080577494","https://openalex.org/W2081028443","https://openalex.org/W2116807840","https://openalex.org/W2505955814","https://openalex.org/W2516900308","https://openalex.org/W2556907171","https://openalex.org/W2754157234","https://openalex.org/W2770482887","https://openalex.org/W2792632122","https://openalex.org/W2794500091","https://openalex.org/W2897236629","https://openalex.org/W2969811770","https://openalex.org/W2972006136","https://openalex.org/W2985489239","https://openalex.org/W3023645647","https://openalex.org/W3036662829","https://openalex.org/W3047301828","https://openalex.org/W3097831474","https://openalex.org/W3112182983","https://openalex.org/W3122850784","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1607269076","https://openalex.org/W2545227774","https://openalex.org/W2953361964","https://openalex.org/W2288349649","https://openalex.org/W4296546724","https://openalex.org/W3200178185","https://openalex.org/W2348706538","https://openalex.org/W2788092364","https://openalex.org/W2259159807","https://openalex.org/W2992056768"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}