{"id":"https://openalex.org/W215355568","doi":"https://doi.org/10.1007/978-3-319-09900-2_4","title":"Noether\u2019s Second Theorem for Variable Order Fractional Variational Problems","display_name":"Noether\u2019s Second Theorem for Variable Order Fractional Variational Problems","publication_year":2014,"publication_date":"2014-08-16","ids":{"openalex":"https://openalex.org/W215355568","doi":"https://doi.org/10.1007/978-3-319-09900-2_4","mag":"215355568"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-09900-2_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-09900-2_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210179954","display_name":"Lecture notes in electrical engineering","issn_l":"1876-1100","issn":["1876-1100","1876-1119"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Electrical Engineering","raw_type":"book-chapter"},"type":"book-chapter","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/A5076441274","display_name":"Agnieszka B. Malinowska","orcid":"https://orcid.org/0000-0002-1309-8583"},"institutions":[{"id":"https://openalex.org/I1323121030","display_name":"Bialystok University of Technology","ror":"https://ror.org/02bzfsy61","country_code":"PL","type":"education","lineage":["https://openalex.org/I1323121030"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Agnieszka B. Malinowska","raw_affiliation_strings":["Faculty of Computer Science, Bialystok University of Technology, 15-351, Bia\u0142ystok, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Bialystok University of Technology, 15-351, Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I1323121030"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078176392","display_name":"Tatiana Odzijewicz","orcid":"https://orcid.org/0000-0002-4354-9293"},"institutions":[{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Tatiana Odzijewicz","raw_affiliation_strings":["Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal"],"affiliations":[{"raw_affiliation_string":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076441274"],"corresponding_institution_ids":["https://openalex.org/I1323121030"],"apc_list":null,"apc_paid":null,"fwci":0.5257,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.767507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"37","last_page":"46"},"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":0.9991999864578247,"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/T10514","display_name":"Numerical methods in engineering","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/noethers-theorem","display_name":"Noether's theorem","score":0.9529803991317749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7048234939575195},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6927576661109924},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6735562086105347},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.48846498131752014},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.44057974219322205},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41979312896728516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38326048851013184},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3513171672821045},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3415282368659973},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.2749025225639343}],"concepts":[{"id":"https://openalex.org/C80892491","wikidata":"https://www.wikidata.org/wiki/Q578555","display_name":"Noether's theorem","level":3,"score":0.9529803991317749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7048234939575195},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6927576661109924},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6735562086105347},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.48846498131752014},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.44057974219322205},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41979312896728516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38326048851013184},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3513171672821045},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3415282368659973},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.2749025225639343},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-09900-2_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-09900-2_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210179954","display_name":"Lecture notes in electrical engineering","issn_l":"1876-1100","issn":["1876-1100","1876-1119"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Electrical Engineering","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W188709132","https://openalex.org/W612687180","https://openalex.org/W629802936","https://openalex.org/W653564841","https://openalex.org/W1215244534","https://openalex.org/W1571391776","https://openalex.org/W1623341677","https://openalex.org/W1966844238","https://openalex.org/W1989306066","https://openalex.org/W2016124038","https://openalex.org/W2016355325","https://openalex.org/W2017663693","https://openalex.org/W2082944446","https://openalex.org/W2121975177","https://openalex.org/W2123921154","https://openalex.org/W2132947505","https://openalex.org/W2155565304","https://openalex.org/W2963985503","https://openalex.org/W3098634140","https://openalex.org/W3099384073","https://openalex.org/W4241728302","https://openalex.org/W4242261367","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4390986594","https://openalex.org/W3102083070","https://openalex.org/W2345828062","https://openalex.org/W4307206163","https://openalex.org/W2885031643","https://openalex.org/W2621061166","https://openalex.org/W3101594837","https://openalex.org/W3101893901","https://openalex.org/W4295095613","https://openalex.org/W1530969180"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}