{"id":"https://openalex.org/W7216765919","doi":null,"title":"Some problems which includes diamond type derivative on time scale","display_name":"Some problems which includes diamond type derivative on time scale","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W7216765919"},"language":"tr","primary_location":{"id":"pmh:oai:openaccess.firat.edu.tr:11508/23711","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11508/23711","pdf_url":null,"source":{"id":"https://openalex.org/S4377196733","display_name":"DSpace - FIRAT (F\u0131rat University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143396566","host_organization_name":"F\u0131rat University","host_organization_lineage":["https://openalex.org/I143396566"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Master Thesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/11508/23711","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003581750","display_name":"Ayse Nur Akk\u0131l\u0131c","orcid":"https://orcid.org/0000-0003-0071-871X","observed_orcids":["https://orcid.org/0000-0003-0071-871X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"AKKILI\u00c7, AY\u015eE NUR","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5003581750"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.49540001153945923,"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":0.49540001153945923,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.4165000021457672,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.035999998450279236,"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/timescales","display_name":"time scales","score":0.8109999895095825},{"id":"https://openalex.org/keywords/sturm-liouville-problems","display_name":"Sturm-Liouville problems","score":0.9440000057220459},{"id":"https://openalex.org/keywords/eigenvalues","display_name":"eigenvalues","score":0.8220000267028809},{"id":"https://openalex.org/keywords/orthogonality-of-eigenfunctions","display_name":"eigenfunction orthogonality","score":0.8610000014305115},{"id":"https://openalex.org/keywords/lagrange-identity","display_name":"Lagrange identity","score":0.7239999771118164},{"id":"https://openalex.org/keywords/green-s-formula","display_name":"Green's formula","score":0.9559999704360962},{"id":"https://openalex.org/keywords/linear-differential-operators","display_name":"linear differential operators","score":0.6539999842643738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5875999927520752},{"id":"https://openalex.org/C2776921476","wikidata":"https://www.wikidata.org/wiki/Q5283","display_name":"Diamond","level":2,"score":0.5626000165939331},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.5296000242233276},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3652999997138977},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.329800009727478},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3127000033855438},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2879999876022339},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.274399995803833}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:openaccess.firat.edu.tr:11508/23711","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11508/23711","pdf_url":null,"source":{"id":"https://openalex.org/S4377196733","display_name":"DSpace - FIRAT (F\u0131rat University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143396566","host_organization_name":"F\u0131rat University","host_organization_lineage":["https://openalex.org/I143396566"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Master Thesis"}],"best_oa_location":{"id":"pmh:oai:openaccess.firat.edu.tr:11508/23711","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11508/23711","pdf_url":null,"source":{"id":"https://openalex.org/S4377196733","display_name":"DSpace - FIRAT (F\u0131rat University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143396566","host_organization_name":"F\u0131rat University","host_organization_lineage":["https://openalex.org/I143396566"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Master Thesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7010988257","https://openalex.org/W7214595077","https://openalex.org/W4392560458","https://openalex.org/W6941403956","https://openalex.org/W7217522809","https://openalex.org/W7219350627","https://openalex.org/W2080047795","https://openalex.org/W464070360","https://openalex.org/W4296095948","https://openalex.org/W7164468528"],"abstract_inverted_index":{"Klasik":[0],"manada":[1],"Sturm-Liouville":[2,17,30,57],"denklemi":[3],"matematiksel":[4],"fizi\u011fin":[5,26],"en":[6,102],"\u00f6nemli":[7],"denklemlerinden":[8],"birisidir.":[9],"Ba\u015flang\u00e7ta,":[10],"\u0131s\u0131":[11],"iletimi":[12],"problemlerinde":[13],"yo\u011fun":[14],"olarak":[15,38],"uygulanan":[16],"teorisi,":[18],"g\u00fcn\u00fcm\u00fczde":[19],"farkl\u0131":[20,66],"fiziksel":[21],"problemlere":[22],"de":[23],"uygulanmaktad\u0131r.":[24],"Matematiksel":[25],"ihtiyac\u0131":[27],"gere\u011fi":[28],"klasik":[29],"probleminde":[31],"farklI":[32],"genelle\u015ftirmeler":[33],"yap\u0131lm\u0131s":[34],"ve":[35,77,95,111,114,117],"buna":[36],"ba\u011fl\u0131":[37],"lineer":[39],"diferensiyel":[40],"operat\u00f6rler":[41],"teorisi":[42],"olu\u015fturulmu\u015ftur.":[43],"Bu":[44,60,121],"\u00e7al\u0131\u015fmada":[45],"ise":[46],"bu":[47],"denklem":[48],"bir":[49,88],"zaman":[50,97],"skalas\u0131nda":[51],"ele":[52,82],"al\u0131narak,":[53],"diamond":[54,107],"alfa":[55,73,92,108],"tipinde":[56,74,93,109],"problemi":[58],"tan\u0131mlanm\u0131\u015ft\u0131r.":[59],"probleme":[61],"ait":[62],"\u00f6zde\u011ferlerin":[63],"basitli\u011fi,":[64],"reelli\u011fi,":[65],"\u00f6zde\u011ferlere":[67],"kar\u015f\u0131l\u0131k":[68],"gelen":[69],"\u00f6z":[70,85,125],"fonksiyonlar\u0131n":[71],"ortogonalli\u011fi,":[72],"Lagrange":[75],"e\u015fitli\u011fi":[76],"Green":[78],"form\u00fcl\u00fc":[79],"verilmi\u015ftir.":[80],"Ayr\u0131ca":[81],"al\u0131nan":[83],"problemin":[84],"fonksiyonlar\u0131":[86],"i\u00e7in":[87],"e\u015fitlik":[89],"bulunmu\u015ftur.":[90],"Diamond":[91],"t\u00fcrev":[94,110,116],"integral":[96],"skalas\u0131n\u0131n":[98],"i\u015flem":[99],"yapma":[100],"a\u00e7\u0131s\u0131ndan":[101],"s\u0131k\u0131nt\u0131l\u0131":[103],"operat\u00f6rleridir.":[104],"Bunun":[105],"nedeni":[106],"integralin":[112],"delta":[113],"nabla":[115],"integralinin":[118],"kombinasyonu":[119],"olmas\u0131d\u0131r.":[120],"a\u00e7\u0131dan":[122],"elde":[123],"edilen":[124],"fonksiyon":[126],"olduk\u00e7a":[127],"\u00f6nemlidir.":[128]},"counts_by_year":[],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2026-10-03T00:00:00"}
