{"id":"https://openalex.org/W4284690158","doi":"https://doi.org/10.1007/s40314-022-01934-y","title":"Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems","display_name":"Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems","publication_year":2022,"publication_date":"2022-07-07","ids":{"openalex":"https://openalex.org/W4284690158","doi":"https://doi.org/10.1007/s40314-022-01934-y"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-022-01934-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-022-01934-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"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":"Computational and Applied 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/A5032731449","display_name":"Tao Guo","orcid":"https://orcid.org/0000-0003-1669-904X"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"T. Guo","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People\u2019s Republic of China","Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0003-1669-904X","affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]},{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People's Republic of China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091026666","display_name":"O. Nikan","orcid":null},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"O. Nikan","raw_affiliation_strings":["School of Mathematics, Iran University of Science and Technology, Tehran, Narmak, Iran"],"raw_orcid":"https://orcid.org/0000-0003-3041-8726","affiliations":[{"raw_affiliation_string":"School of Mathematics, Iran University of Science and Technology, Tehran, Narmak, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015962889","display_name":"Z. Avazzadeh","orcid":"https://orcid.org/0000-0003-2257-1798"},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Z. Avazzadeh","raw_affiliation_strings":["Department of Applied Mathematics, Xi\u2019an Jiaotong-Liverpool University, Suzhou, 215123, China","Department of Applied Mathematics, Xi'an Jiaotong-Liverpool University, Suzhou, 215123, China"],"raw_orcid":"https://orcid.org/0000-0003-2257-1798","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Xi\u2019an Jiaotong-Liverpool University, Suzhou, 215123, China","institution_ids":["https://openalex.org/I69356397"]},{"raw_affiliation_string":"Department of Applied Mathematics, Xi'an Jiaotong-Liverpool University, Suzhou, 215123, China","institution_ids":["https://openalex.org/I69356397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055795823","display_name":"Wenlin Qiu","orcid":"https://orcid.org/0000-0003-1144-5315"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"W. Qiu","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People\u2019s Republic of China","Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0003-1144-5315","affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]},{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People's Republic of China","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015962889"],"corresponding_institution_ids":["https://openalex.org/I69356397"],"apc_list":null,"apc_paid":null,"fwci":5.9544,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.97668951,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"41","issue":"6","first_page":null,"last_page":null},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9970999956130981,"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/T10514","display_name":"Numerical methods in engineering","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7709070444107056},{"id":"https://openalex.org/keywords/alternating-direction-implicit-method","display_name":"Alternating direction implicit method","score":0.618192195892334},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.603401780128479},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5883145332336426},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5859618782997131},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5763866305351257},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5331873893737793},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.49543297290802},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.462875634431839},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4483977258205414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3231112062931061},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.320476233959198},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31365397572517395}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7709070444107056},{"id":"https://openalex.org/C142363948","wikidata":"https://www.wikidata.org/wiki/Q4736413","display_name":"Alternating direction implicit method","level":3,"score":0.618192195892334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.603401780128479},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5883145332336426},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5859618782997131},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5763866305351257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5331873893737793},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.49543297290802},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.462875634431839},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4483977258205414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3231112062931061},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.320476233959198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31365397572517395},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-022-01934-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-022-01934-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W374977727","https://openalex.org/W833140947","https://openalex.org/W1633561672","https://openalex.org/W1981340038","https://openalex.org/W1991982189","https://openalex.org/W1992715714","https://openalex.org/W1995597760","https://openalex.org/W2001011967","https://openalex.org/W2006281429","https://openalex.org/W2008947598","https://openalex.org/W2035830378","https://openalex.org/W2053796073","https://openalex.org/W2059607966","https://openalex.org/W2060694043","https://openalex.org/W2083488564","https://openalex.org/W2083834253","https://openalex.org/W2086512227","https://openalex.org/W2107162131","https://openalex.org/W2137120557","https://openalex.org/W2188779374","https://openalex.org/W2304262673","https://openalex.org/W2338894593","https://openalex.org/W2368199140","https://openalex.org/W2510459129","https://openalex.org/W2519029477","https://openalex.org/W2787959293","https://openalex.org/W2790820636","https://openalex.org/W2808923703","https://openalex.org/W2919494258","https://openalex.org/W2950875508","https://openalex.org/W2963020731","https://openalex.org/W2971942511","https://openalex.org/W3033138970","https://openalex.org/W3043159494","https://openalex.org/W3098900206","https://openalex.org/W3109681878","https://openalex.org/W3111515545","https://openalex.org/W3148434010","https://openalex.org/W3160514375","https://openalex.org/W3165867195","https://openalex.org/W3169314196","https://openalex.org/W3179760003","https://openalex.org/W3185989456","https://openalex.org/W3193732826","https://openalex.org/W3209219424","https://openalex.org/W3210605737","https://openalex.org/W3210977280","https://openalex.org/W3212770959","https://openalex.org/W4200005720","https://openalex.org/W4213067792","https://openalex.org/W4301223505"],"related_works":["https://openalex.org/W2083355284","https://openalex.org/W2166601248","https://openalex.org/W1697484951","https://openalex.org/W4297084911","https://openalex.org/W3123568166","https://openalex.org/W4298930346","https://openalex.org/W4226238329","https://openalex.org/W4361230184","https://openalex.org/W3151491349","https://openalex.org/W1971414248"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}