{"id":"https://openalex.org/W3087046292","doi":"https://doi.org/10.1186/s13662-024-03856-x","title":"On the existence-uniqueness and exponential estimate for solutions to stochastic functional differential equations driven by G-L\u00e9vy process","display_name":"On the existence-uniqueness and exponential estimate for solutions to stochastic functional differential equations driven by G-L\u00e9vy process","publication_year":2025,"publication_date":"2025-01-07","ids":{"openalex":"https://openalex.org/W3087046292","doi":"https://doi.org/10.1186/s13662-024-03856-x","mag":"3087046292"},"language":"en","primary_location":{"id":"doi:10.1186/s13662-024-03856-x","doi":"https://doi.org/10.1186/s13662-024-03856-x","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13662-024-03856-x","pdf_url":"https://link.springer.com/content/pdf/10.1186/s13662-024-03856-x.pdf","source":{"id":"https://openalex.org/S4210218429","display_name":"Advances in Continuous and Discrete Models","issn_l":"2731-4235","issn":["2731-4235"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","norway-1","oarl","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Continuous and Discrete Models","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1186/s13662-024-03856-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048775283","display_name":"Rahman Ullah","orcid":"https://orcid.org/0000-0001-7554-3358","observed_orcids":["https://orcid.org/0000-0001-7554-3358"]},"institutions":[{"id":"https://openalex.org/I4210122157","display_name":"Hubei Polytechnic University","ror":"https://ror.org/01z07eq06","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210122157"]},{"id":"https://openalex.org/I4387153791","display_name":"Women University Swabi","ror":"https://ror.org/00f98bm36","country_code":"PK","type":"education","lineage":["https://openalex.org/I4387153791"]}],"countries":["CN","PK"],"is_corresponding":true,"raw_author_name":"Rahman Ullah","raw_affiliation_strings":["Department of Mathematics and Statistics, Women University Swabi, Swabi, 23430, Pakistan","School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Women University Swabi, Swabi, 23430, Pakistan","institution_ids":["https://openalex.org/I4387153791"]},{"raw_affiliation_string":"School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China","institution_ids":["https://openalex.org/I4210122157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036931298","display_name":"Faiz Faizullah","orcid":"https://orcid.org/0000-0001-7474-7754","observed_orcids":["https://orcid.org/0000-0001-7474-7754","https://orcid.org/0000-0003-2477-7458"]},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Faiz Faizullah","raw_affiliation_strings":["Department of BS&H, College of E&ME, National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of BS&H, College of E&ME, National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061800733","display_name":"Ihteram Ali","orcid":"https://orcid.org/0000-0002-6765-1559","observed_orcids":["https://orcid.org/0000-0002-6765-1559"]},"institutions":[{"id":"https://openalex.org/I4387153791","display_name":"Women University Swabi","ror":"https://ror.org/00f98bm36","country_code":"PK","type":"education","lineage":["https://openalex.org/I4387153791"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ihteram Ali","raw_affiliation_strings":["Department of Mathematics and Statistics, Women University Swabi, Swabi, 23430, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Women University Swabi, Swabi, 23430, Pakistan","institution_ids":["https://openalex.org/I4387153791"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Muhammad Farooq","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Farooq","raw_affiliation_strings":["Department of BS&H, College of E&ME, National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of BS&H, College of E&ME, National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103875639","display_name":"MA Rana","orcid":"https://orcid.org/0000-0001-9445-8861","observed_orcids":["https://orcid.org/0000-0001-9445-8861"]},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. A. Rana","raw_affiliation_strings":["Department of Mathematics and Statistics, Riphah International University Islamabad, Islamabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Riphah International University Islamabad, Islamabad, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007665126","display_name":"Fuad A. A. Awwad","orcid":"https://orcid.org/0000-0001-9541-5695","observed_orcids":["https://orcid.org/0000-0001-9541-5695"]},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fuad A. Awwad","raw_affiliation_strings":["Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh, 11587, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh, 11587, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5036931298","https://openalex.org/A5048775283"],"corresponding_institution_ids":["https://openalex.org/I4210122157","https://openalex.org/I4387153791","https://openalex.org/I929597975"],"apc_list":{"value":1890,"currency":"USD","value_usd":1890},"apc_paid":{"value":1890,"currency":"USD","value_usd":1890},"fwci":3.1532,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.90215101,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.7724999785423279,"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"}},"topics":[{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.7724999785423279,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.18359999358654022,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.028699999675154686,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-functional-differential-equations","display_name":"stochastic functional differential equations","score":1.0},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.9190000295639038},{"id":"https://openalex.org/keywords/exponential-estimates","display_name":"exponential estimates","score":0.640999972820282},{"id":"https://openalex.org/keywords/error-estimation","display_name":"error estimation","score":0.8500000238418579},{"id":"https://openalex.org/keywords/stochastic-dynamical-systems","display_name":"stochastic dynamical systems","score":0.5879999995231628}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8379775285720825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5989583730697632},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5930917263031006},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.589924693107605},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5804177522659302},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.47940322756767273},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44560304284095764},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4243625998497009},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38196831941604614},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17590880393981934},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14672988653182983},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08184641599655151},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1186/s13662-024-03856-x","doi":"https://doi.org/10.1186/s13662-024-03856-x","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13662-024-03856-x","pdf_url":"https://link.springer.com/content/pdf/10.1186/s13662-024-03856-x.pdf","source":{"id":"https://openalex.org/S4210218429","display_name":"Advances in Continuous and Discrete Models","issn_l":"2731-4235","issn":["2731-4235"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","norway-1","oarl","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Continuous and Discrete Models","raw_type":"journal-article"},{"id":"doi:10.48550/arxiv.2005.01930","doi":"https://doi.org/10.48550/arxiv.2005.01930","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.01930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:3087046292","doi":null,"is_oa":false,"landing_page_url":"https://ui.adsabs.harvard.edu/abs/2020arXiv200501930F/abstract","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1186/s13662-024-03856-x","doi":"https://doi.org/10.1186/s13662-024-03856-x","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13662-024-03856-x","pdf_url":"https://link.springer.com/content/pdf/10.1186/s13662-024-03856-x.pdf","source":{"id":"https://openalex.org/S4210218429","display_name":"Advances in Continuous and Discrete Models","issn_l":"2731-4235","issn":["2731-4235"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","norway-1","oarl","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Continuous and Discrete Models","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3087046292.pdf","grobid_xml":"https://content.openalex.org/works/W3087046292.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W983956578","https://openalex.org/W1494536455","https://openalex.org/W1965761524","https://openalex.org/W1980323976","https://openalex.org/W1987896787","https://openalex.org/W1992382156","https://openalex.org/W1996013576","https://openalex.org/W2004044229","https://openalex.org/W2016116013","https://openalex.org/W2062114931","https://openalex.org/W2334081561","https://openalex.org/W2483461032","https://openalex.org/W2605501408","https://openalex.org/W2755466688","https://openalex.org/W2765081439","https://openalex.org/W2765548013","https://openalex.org/W2783871869","https://openalex.org/W2784730055","https://openalex.org/W3004816399","https://openalex.org/W3142426491","https://openalex.org/W4396738227"],"related_works":["https://openalex.org/W3021106504","https://openalex.org/W4366770982","https://openalex.org/W2809475151","https://openalex.org/W2783871869","https://openalex.org/W7159638347","https://openalex.org/W1980323976","https://openalex.org/W3211516913","https://openalex.org/W4320523378","https://openalex.org/W2590341693","https://openalex.org/W2966114010"],"abstract_inverted_index":{"The":[0],"existence-uniqueness":[1,40],"theory":[2,25],"for":[3,26,42],"solutions":[4,43,65],"to":[5,22,44],"stochastic":[6,27],"dynamic":[7],"systems":[8],"is":[9],"always":[10],"a":[11],"significant":[12],"theme":[13],"and":[14,62],"has":[15,74],"received":[16],"tremendous":[17],"attention.":[18],"This":[19],"article":[20],"aims":[21],"study":[23],"the":[24,34,39,48,54,58,71],"functional":[28],"differential":[29],"equations":[30],"(SFDEs)":[31],"driven":[32,46],"by":[33,47],"G-L\u00e9vy":[35,49],"process.":[36,50],"It":[37],"derives":[38],"theorem":[41],"SFDEs":[45],"Moreover,":[51],"it":[52],"shows":[53],"error":[55],"estimation":[56],"between":[57],"exact":[59],"solution":[60],"$x(t)$":[61],"Picard":[63],"approximate":[64],"$x^{n}(t),":[66],"n\\geq":[67],"1$":[68],".":[69],"Ultimately,":[70],"exponential":[72],"estimate":[73],"been":[75],"derived.":[76]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-09-25T00:00:00"}
