{"id":"https://openalex.org/W4296792124","doi":"https://doi.org/10.1155/2022/2661343","title":"Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability","display_name":"Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability","publication_year":2022,"publication_date":"2022-09-23","ids":{"openalex":"https://openalex.org/W4296792124","doi":"https://doi.org/10.1155/2022/2661343"},"language":"tl","primary_location":{"id":"doi:10.1155/2022/2661343","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/2661343","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/2661343.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2022/2661343.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037407023","display_name":"Naz\u0131m I. Mahmudov","orcid":"https://orcid.org/0000-0003-3943-1732"},"institutions":[{"id":"https://openalex.org/I36515993","display_name":"Eastern Mediterranean University","ror":"https://ror.org/00excyz84","country_code":"CY","type":"education","lineage":["https://openalex.org/I36515993"]}],"countries":["CY"],"is_corresponding":true,"raw_author_name":"Nazim I. Mahmudov","raw_affiliation_strings":["Department of Mathematics, Eastern Mediterranean University, Famagusta, 99628 Northern Cyprus, Mersin 10, Turkey"],"raw_orcid":"https://orcid.org/0000-0003-3943-1732","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Eastern Mediterranean University, Famagusta, 99628 Northern Cyprus, Mersin 10, Turkey","institution_ids":["https://openalex.org/I36515993"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037407023"],"corresponding_institution_ids":["https://openalex.org/I36515993"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.5003,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62381443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2022","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9864000082015991,"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"}},"topics":[{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9864000082015991,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9797999858856201,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9775000214576721,"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/type","display_name":"Type (biology)","score":0.5398013591766357},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4849557876586914}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5398013591766357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4849557876586914},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2022/2661343","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/2661343","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/2661343.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a38f9c31f80040bbbbe8564a46a3910c","is_oa":true,"landing_page_url":"https://doaj.org/article/a38f9c31f80040bbbbe8564a46a3910c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/2661343","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/2661343","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/2661343.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4296792124.pdf","grobid_xml":"https://content.openalex.org/works/W4296792124.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1139833940","https://openalex.org/W1978711257","https://openalex.org/W1995594233","https://openalex.org/W2006561420","https://openalex.org/W2013518448","https://openalex.org/W2030947806","https://openalex.org/W2040413858","https://openalex.org/W2064722800","https://openalex.org/W2077696055","https://openalex.org/W2095209033","https://openalex.org/W2118849038","https://openalex.org/W2520807814","https://openalex.org/W2527573171","https://openalex.org/W2763053696","https://openalex.org/W2910688993","https://openalex.org/W2962892865","https://openalex.org/W2964267535","https://openalex.org/W3067061738","https://openalex.org/W3081717202","https://openalex.org/W3097473881","https://openalex.org/W3098837047","https://openalex.org/W4220724890","https://openalex.org/W4281680349","https://openalex.org/W4286628171","https://openalex.org/W4288099489","https://openalex.org/W4296792124"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"introduce":[1],"the":[2,17,26,75],"delayed":[3,8,12],"Mittag-Leffler":[4],"type":[5,31,53,77,90],"matrix":[6],"functions,":[7],"fractional":[9,13,32,78,91,103],"cosine,":[10],"and":[11,15,52,64,88,98],"sine":[14],"use":[16],"Laplace":[18],"transform":[19],"to":[20,25],"obtain":[21],"an":[22],"analytical":[23],"solution":[24],"IVP":[27],"for":[28,86,101],"a":[29],"Hilfer":[30,76],"linear":[33,79,92],"time-delay":[34,80,93],"system":[35],"D0,t\u03bc,\u03bdzt+Azt+\u03a9zt\u2212h=ft":[46],"of":[47,74],"order":[48],"1<\u03bc<2":[51],"0\u2264\u03bd\u22641":[56],",":[57],"with":[58,95],"nonpermutable":[59],"matrices":[60,97],"A":[63],"\u03a9":[67],".":[68],"Moreover,":[69],"we":[70],"study":[71],"Ulam-Hyers":[72],"stability":[73],"system.":[81],"Obtained":[82],"results":[83],"extend":[84],"those":[85],"Caputo":[87],"Riemann-Liouville":[89],"systems":[94],"permutable":[96],"new":[99],"even":[100],"these":[102],"delay":[104],"systems.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}