{"id":"https://openalex.org/W2736102016","doi":"https://doi.org/10.11121/ijocta.01.2017.00360","title":"Numerical solution of neutral functional-differential equations with proportional delays","display_name":"Numerical solution of neutral functional-differential equations with proportional delays","publication_year":2017,"publication_date":"2017-07-14","ids":{"openalex":"https://openalex.org/W2736102016","doi":"https://doi.org/10.11121/ijocta.01.2017.00360","mag":"2736102016"},"language":"en","primary_location":{"id":"doi:10.11121/ijocta.01.2017.00360","doi":"https://doi.org/10.11121/ijocta.01.2017.00360","is_oa":true,"landing_page_url":"https://doi.org/10.11121/ijocta.01.2017.00360","pdf_url":null,"source":{"id":"https://openalex.org/S2738277457","display_name":"An International Journal of Optimization and Control Theories & Applications (IJOCTA)","issn_l":"2146-0957","issn":["2146-0957","2146-5703"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310318307","host_organization_name":"Bal\u0131kesir University","host_organization_lineage":["https://openalex.org/P4310318307"],"host_organization_lineage_names":["Bal\u0131kesir University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"An International Journal of Optimization and Control: Theories &amp; Applications (IJOCTA)","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2736102016"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.11121/ijocta.01.2017.00360","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061676774","display_name":"Mehmet Giyas Sakar","orcid":"https://orcid.org/0000-0002-1911-2622","observed_orcids":["https://orcid.org/0000-0002-1911-2622"]},"institutions":[{"id":"https://openalex.org/I118567650","display_name":"Van Y\u00fcz\u00fcnc\u00fc Y\u0131l \u00dcniversitesi","ror":"https://ror.org/041jyzp61","country_code":"TR","type":"education","lineage":["https://openalex.org/I118567650"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Mehmet Giyas Sakar","raw_affiliation_strings":["Yuzuncu Yil University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yuzuncu Yil University","institution_ids":["https://openalex.org/I118567650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061676774"],"corresponding_institution_ids":["https://openalex.org/I118567650"],"apc_list":null,"apc_paid":null,"fwci":0.8348,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.70602808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"7","issue":"2","first_page":"186","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.6269999742507935,"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":0.6269999742507935,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.24240000545978546,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.07069999724626541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/neutral-functional-differential-equations","display_name":"neutral functional differential equations","score":0.9869999885559082},{"id":"https://openalex.org/keywords/proportional-delay","display_name":"proportional delay","score":0.972000002861023},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"homotopy analysis method","score":0.9950000047683716},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.9980000257492065},{"id":"https://openalex.org/keywords/error-estimates","display_name":"error estimates","score":0.703000009059906},{"id":"https://openalex.org/keywords/numerical-solution","display_name":"numerical solution","score":0.7910000085830688}],"concepts":[{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.8510724306106567},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.6926324367523193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6840200424194336},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5817340612411499},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5782241821289062},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5670972466468811},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5458342432975769},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5234555602073669},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.48808300495147705},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.48594653606414795},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.48543649911880493},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43090420961380005},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32924574613571167},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1937476396560669},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1787700057029724},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07798698544502258},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.11121/ijocta.01.2017.00360","doi":"https://doi.org/10.11121/ijocta.01.2017.00360","is_oa":true,"landing_page_url":"https://doi.org/10.11121/ijocta.01.2017.00360","pdf_url":null,"source":{"id":"https://openalex.org/S2738277457","display_name":"An International Journal of Optimization and Control Theories & Applications (IJOCTA)","issn_l":"2146-0957","issn":["2146-0957","2146-5703"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310318307","host_organization_name":"Bal\u0131kesir University","host_organization_lineage":["https://openalex.org/P4310318307"],"host_organization_lineage_names":["Bal\u0131kesir University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"An International Journal of Optimization and Control: Theories &amp; Applications (IJOCTA)","raw_type":"journal-article"},{"id":"pmh:fe1cd059-6930-40ae-8c89-a652051f1b96","doi":null,"is_oa":false,"landing_page_url":"https://avesis.yyu.edu.tr/publication/details/fe1cd059-6930-40ae-8c89-a652051f1b96/oai","pdf_url":null,"source":{"id":"https://openalex.org/S7407055328","display_name":"Van Y\u00fcz\u00fcnc\u00fc Y\u0131l University Academic Data Management System","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.11121/ijocta.01.2017.00360","doi":"https://doi.org/10.11121/ijocta.01.2017.00360","is_oa":true,"landing_page_url":"https://doi.org/10.11121/ijocta.01.2017.00360","pdf_url":null,"source":{"id":"https://openalex.org/S2738277457","display_name":"An International Journal of Optimization and Control Theories & Applications (IJOCTA)","issn_l":"2146-0957","issn":["2146-0957","2146-5703"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310318307","host_organization_name":"Bal\u0131kesir University","host_organization_lineage":["https://openalex.org/P4310318307"],"host_organization_lineage_names":["Bal\u0131kesir University"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"An International Journal of Optimization and Control: Theories &amp; Applications (IJOCTA)","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1964333834","https://openalex.org/W1973075722","https://openalex.org/W1976196891","https://openalex.org/W1981827551","https://openalex.org/W2028275757","https://openalex.org/W2038376973","https://openalex.org/W2038496690","https://openalex.org/W2047173892","https://openalex.org/W2049589825","https://openalex.org/W2057768486","https://openalex.org/W2068097649","https://openalex.org/W2077095261","https://openalex.org/W2082114337","https://openalex.org/W2082565636","https://openalex.org/W2084354765","https://openalex.org/W2095151500","https://openalex.org/W2119794696","https://openalex.org/W2168825792","https://openalex.org/W2281564558"],"related_works":["https://openalex.org/W7132257710","https://openalex.org/W2028275757","https://openalex.org/W3084867261","https://openalex.org/W2047173892","https://openalex.org/W4391575326","https://openalex.org/W2487139189","https://openalex.org/W2131246131","https://openalex.org/W3010010862","https://openalex.org/W2560301827","https://openalex.org/W2038496690"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"homotopy":[3,57],"analysis":[4,30,58],"method":[5,35,59],"is":[6,64],"improved":[7],"with":[8,26,47,60],"optimal":[9],"determination":[10],"of":[11,16,34],"auxiliary":[12],"parameter":[13],"by":[14],"use":[15],"residual":[17,61],"error":[18,32,62],"function":[19,63],"for":[20],"solving":[21],"neutral":[22],"functional-differential":[23],"equations":[24],"(NFDEs)":[25],"proportional":[27],"delays.":[28],"Convergence":[29],"and":[31,43,67],"estimate":[33],"are":[36,41,45],"given.":[37],"Some":[38],"numerical":[39,52],"examples":[40],"solved":[42],"comparisons":[44],"made":[46],"the":[48,56],"existing":[49],"results.":[50],"The":[51],"results":[53],"show":[54],"that":[55],"very":[65],"effective":[66],"simple.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2017-07-21T00:00:00"}
