{"id":"https://openalex.org/W2955902581","doi":"https://doi.org/10.1137/17m1121354","title":"Dissipativity and Contractivity Analysis for Fractional Functional Differential Equations and their Numerical Approximations","display_name":"Dissipativity and Contractivity Analysis for Fractional Functional Differential Equations and their Numerical Approximations","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2955902581","doi":"https://doi.org/10.1137/17m1121354","mag":"2955902581"},"language":"en","primary_location":{"id":"doi:10.1137/17m1121354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1121354","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5037198617","display_name":"Dongling Wang","orcid":"https://orcid.org/0000-0001-8509-2837"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dongling Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090609331","display_name":"Jun Zou","orcid":"https://orcid.org/0000-0002-4809-7724"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun Zou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4313,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.89020537,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"57","issue":"3","first_page":"1445","last_page":"1470"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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":0.9218400120735168},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6079214215278625},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4896555542945862},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48523974418640137},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47289907932281494},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.4566376507282257},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43773573637008667},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43365564942359924},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4333633482456207},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41734522581100464},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.41624781489372253}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9218400120735168},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6079214215278625},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4896555542945862},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48523974418640137},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47289907932281494},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.4566376507282257},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43773573637008667},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43365564942359924},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4333633482456207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41734522581100464},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.41624781489372253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1121354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1121354","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2157508914","display_name":null,"funder_award_id":"11501447","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G854489041","display_name":null,"funder_award_id":"11871057","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1535168513","https://openalex.org/W1964106719","https://openalex.org/W1967595729","https://openalex.org/W1969312973","https://openalex.org/W1970786191","https://openalex.org/W1972474856","https://openalex.org/W1974267666","https://openalex.org/W1975939301","https://openalex.org/W1981981778","https://openalex.org/W2000422023","https://openalex.org/W2001011967","https://openalex.org/W2004202105","https://openalex.org/W2005114389","https://openalex.org/W2005940931","https://openalex.org/W2013958055","https://openalex.org/W2024099978","https://openalex.org/W2029851266","https://openalex.org/W2032918469","https://openalex.org/W2044611344","https://openalex.org/W2057119166","https://openalex.org/W2057173171","https://openalex.org/W2060452322","https://openalex.org/W2063898196","https://openalex.org/W2070438803","https://openalex.org/W2074903192","https://openalex.org/W2092861539","https://openalex.org/W2094551465","https://openalex.org/W2103999702","https://openalex.org/W2107162131","https://openalex.org/W2120075729","https://openalex.org/W2152721142","https://openalex.org/W2165076033","https://openalex.org/W2173131798","https://openalex.org/W2343137341","https://openalex.org/W2487182418","https://openalex.org/W2510732450","https://openalex.org/W2511264644","https://openalex.org/W2567244142","https://openalex.org/W2567477586","https://openalex.org/W2619423951","https://openalex.org/W3104385214","https://openalex.org/W4253062931"],"related_works":["https://openalex.org/W2102789413","https://openalex.org/W2096467061","https://openalex.org/W1532287630","https://openalex.org/W2940603871","https://openalex.org/W2052500721","https://openalex.org/W2082296130","https://openalex.org/W4299508867","https://openalex.org/W4226214462","https://openalex.org/W2028331352","https://openalex.org/W2475429613"],"abstract_inverted_index":{"We":[0],"first":[1],"present":[2],"a":[3,30],"new":[4],"delay-dependent":[5],"fractional":[6,17,64,110,114,118],"generalization":[7],"of":[8,16,27,41,105,132,145],"Halanay-like":[9],"inequality":[10],"to":[11,79,101,128],"characterize":[12],"the":[13,25,35,39,71,87,92,109,130,133,142,149],"asymptotic":[14,36],"behavior":[15],"functional":[18,72],"differential":[19,112],"equations":[20],"(F-FDEs).":[21],"Then":[22],"we":[23,139],"study":[24],"dissipativity":[26],"F-FDEs":[28,42,54,154],"with":[29,43,67],"bounded":[31],"absorbing":[32],"set":[33],"and":[34,38,59,82,84,117,148,155,163],"stability":[37],"contractivity":[40],"algebraically":[44],"contractive":[45,83],"rate.":[46],"Two":[47],"numerical":[48,124,135,143],"schemes":[49,76,147,159],"are":[50,77,126,160],"further":[51],"constructed":[52],"for":[53,62,70,153,166],"based":[55],"on":[56],"Gr\u00fcnwald--Letnikov":[57],"formula":[58],"$L1$":[60],"method":[61],"Caputo":[63],"derivative,":[65],"together":[66],"linear":[68],"interpolation":[69],"terms.":[73],"These":[74,95],"two":[75],"proved":[78],"be":[80,98],"dissipative":[81],"can":[85,97],"preserve":[86],"exact":[88],"decay":[89],"rate":[90],"as":[91,108],"continuous":[93],"equations.":[94,121],"results":[96],"directly":[99],"applied":[100],"some":[102,167],"special":[103],"cases":[104],"F-FDEs,":[106],"such":[107],"delay":[111,119],"equations,":[113,116],"integro-differential":[115,120],"Finally,":[122],"several":[123],"examples":[125],"given":[127],"illustrate":[129],"advantages":[131],"structure-preserving":[134],"methods.":[136],"In":[137],"particular,":[138],"shall":[140],"compare":[141],"performance":[144],"our":[146,158],"popular":[150],"predictor-corrector":[151],"algorithms":[152],"demonstrate":[156],"that":[157],"more":[161],"efficient":[162],"robust,":[164],"especially":[165],"stiff":[168],"systems.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}