{"id":"https://openalex.org/W4200160939","doi":"https://doi.org/10.3390/sym13122434","title":"Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients","display_name":"Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients","publication_year":2021,"publication_date":"2021-12-16","ids":{"openalex":"https://openalex.org/W4200160939","doi":"https://doi.org/10.3390/sym13122434"},"language":"en","primary_location":{"id":"doi:10.3390/sym13122434","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122434","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2434/pdf?version=1639628504","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/12/2434/pdf?version=1639628504","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101452708","display_name":"Ruixin Li","orcid":"https://orcid.org/0009-0009-0726-9882"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruixin Li","raw_affiliation_strings":["School of Science, Jiangnan University, Wuxi 214122, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Jiangnan University, Wuxi 214122, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017499777","display_name":"Lianzhong Li","orcid":null},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lianzhong Li","raw_affiliation_strings":["School of Science, Jiangnan University, Wuxi 214122, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Jiangnan University, Wuxi 214122, China","institution_ids":["https://openalex.org/I111599522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017499777"],"corresponding_institution_ids":["https://openalex.org/I111599522"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.2319,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52030239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"12","first_page":"2434","last_page":"2434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/conservation-law","display_name":"Conservation law","score":0.7761331796646118},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.7425407767295837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5875336527824402},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45730119943618774},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4491795599460602},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4357709288597107},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.42817223072052},{"id":"https://openalex.org/keywords/virtue","display_name":"Virtue","score":0.42247089743614197},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.40053409337997437},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3719262480735779},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.2617073953151703},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07431477308273315}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7761331796646118},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.7425407767295837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5875336527824402},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45730119943618774},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4491795599460602},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4357709288597107},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.42817223072052},{"id":"https://openalex.org/C2777239683","wikidata":"https://www.wikidata.org/wiki/Q157811","display_name":"Virtue","level":2,"score":0.42247089743614197},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40053409337997437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3719262480735779},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.2617073953151703},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07431477308273315},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13122434","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122434","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2434/pdf?version=1639628504","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f36bc10a00674e60ab95ed393d78ac4c","is_oa":true,"landing_page_url":"https://doaj.org/article/f36bc10a00674e60ab95ed393d78ac4c","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":"Symmetry, Vol 13, Iss 12, p 2434 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/12/2434/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13122434","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 13; Issue 12; Pages: 2434","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13122434","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122434","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2434/pdf?version=1639628504","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7300000190734863,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200160939.pdf","grobid_xml":"https://content.openalex.org/works/W4200160939.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1975670568","https://openalex.org/W1981768738","https://openalex.org/W1992619775","https://openalex.org/W2001748301","https://openalex.org/W2011301580","https://openalex.org/W2031978882","https://openalex.org/W2045979957","https://openalex.org/W2069050392","https://openalex.org/W2072058477","https://openalex.org/W2085413857","https://openalex.org/W2085668771","https://openalex.org/W2094590320","https://openalex.org/W2561021860","https://openalex.org/W2583893687","https://openalex.org/W2598100571","https://openalex.org/W2765689481","https://openalex.org/W2767618852","https://openalex.org/W2806527270","https://openalex.org/W2883715470","https://openalex.org/W2887643689","https://openalex.org/W2921652470","https://openalex.org/W2985178249","https://openalex.org/W3005875510","https://openalex.org/W3007669355","https://openalex.org/W3118384204","https://openalex.org/W3128356427","https://openalex.org/W4247953052","https://openalex.org/W6644300598","https://openalex.org/W6645947228","https://openalex.org/W6661215120","https://openalex.org/W6753966058","https://openalex.org/W6790660013","https://openalex.org/W6828014654"],"related_works":["https://openalex.org/W2376913909","https://openalex.org/W579813788","https://openalex.org/W3084056392","https://openalex.org/W2385074746","https://openalex.org/W2378622502","https://openalex.org/W2378706131","https://openalex.org/W2097165408","https://openalex.org/W1570462502","https://openalex.org/W2355987749","https://openalex.org/W2079321792"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"employ":[4],"the":[5,14,29,33,37,50,54],"certain":[6],"theory":[7],"of":[8,32,49],"Lie":[9,22],"symmetry":[10,24,30],"analysis":[11],"to":[12,27],"discuss":[13],"time-fractional":[15],"Gardner":[16],"equation":[17],"with":[18],"time-dependent":[19],"coefficients.":[20],"The":[21],"point":[23],"is":[25],"applied":[26],"realize":[28],"reduction":[31],"equation,":[34],"and":[35],"then":[36],"power":[38],"series":[39],"solutions":[40],"in":[41],"some":[42],"specific":[43],"cases":[44],"are":[45,57],"obtained.":[46],"By":[47],"virtue":[48],"fractional":[51],"conservation":[52,55],"theorem,":[53],"laws":[56],"constructed.":[58]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
