{"id":"https://openalex.org/W3032990393","doi":"https://doi.org/10.3390/axioms9020065","title":"Generalized Nabla Differentiability and Integrability for Fuzzy Functions on Time Scales","display_name":"Generalized Nabla Differentiability and Integrability for Fuzzy Functions on Time Scales","publication_year":2020,"publication_date":"2020-06-08","ids":{"openalex":"https://openalex.org/W3032990393","doi":"https://doi.org/10.3390/axioms9020065","mag":"3032990393"},"language":"en","primary_location":{"id":"doi:10.3390/axioms9020065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9020065","pdf_url":"https://www.mdpi.com/2075-1680/9/2/65/pdf?version=1593497733","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/9/2/65/pdf?version=1593497733","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003738833","display_name":"R. Leelavathi","orcid":null},"institutions":[{"id":"https://openalex.org/I875944469","display_name":"Koneru Lakshmaiah Education Foundation","ror":"https://ror.org/02k949197","country_code":"IN","type":"education","lineage":["https://openalex.org/I875944469"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"R. Leelavathi","raw_affiliation_strings":["Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram 522502, Guntur, Andhra Pradesh, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram 522502, Guntur, Andhra Pradesh, India","institution_ids":["https://openalex.org/I875944469"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062351903","display_name":"G. Suresh Kumar","orcid":"https://orcid.org/0000-0001-8987-4705"},"institutions":[{"id":"https://openalex.org/I875944469","display_name":"Koneru Lakshmaiah Education Foundation","ror":"https://ror.org/02k949197","country_code":"IN","type":"education","lineage":["https://openalex.org/I875944469"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"G. Suresh Kumar","raw_affiliation_strings":["Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram 522502, Guntur, Andhra Pradesh, India"],"raw_orcid":"https://orcid.org/0000-0001-8987-4705","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram 522502, Guntur, Andhra Pradesh, India","institution_ids":["https://openalex.org/I875944469"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055431798","display_name":"Ravi P. Agarwal","orcid":"https://orcid.org/0000-0003-0634-2370"},"institutions":[{"id":"https://openalex.org/I181414168","display_name":"Texas A&M University \u2013 Kingsville","ror":"https://ror.org/05abs3w97","country_code":"US","type":"education","lineage":["https://openalex.org/I181414168"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ravi P. Agarwal","raw_affiliation_strings":["Department of Mathematics, Texas A&amp;M University-Kingsville, Kingsville, TX 78363-8202, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&amp;M University-Kingsville, Kingsville, TX 78363-8202, USA","institution_ids":["https://openalex.org/I181414168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100773459","display_name":"Chao Wang","orcid":"https://orcid.org/0000-0002-6357-3661"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Wang","raw_affiliation_strings":["Department of Mathematics, Yunnan University, Kunming 650091, China"],"raw_orcid":"https://orcid.org/0000-0002-6357-3661","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yunnan University, Kunming 650091, China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072355722","display_name":"M. S. N. Murty","orcid":"https://orcid.org/0000-0003-4996-3636"},"institutions":[{"id":"https://openalex.org/I1287339526","display_name":"Reserve Bank of India","ror":"https://ror.org/04w0b7z78","country_code":"IN","type":"other","lineage":["https://openalex.org/I1287339526"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"M.S.N. Murty","raw_affiliation_strings":["Sainivas, D.No. 21-47, Opp. State Bank of India, Bank Street, Nuzvid 521201, Krishna, Andhra Pradesh, India"],"raw_orcid":"https://orcid.org/0000-0003-4996-3636","affiliations":[{"raw_affiliation_string":"Sainivas, D.No. 21-47, Opp. State Bank of India, Bank Street, Nuzvid 521201, Krishna, Andhra Pradesh, India","institution_ids":["https://openalex.org/I1287339526"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5055431798"],"corresponding_institution_ids":["https://openalex.org/I181414168"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.443,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65165119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"2","first_page":"65","last_page":"65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9983999729156494,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9901000261306763,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.9625427722930908},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.8760912418365479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.742415189743042},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6684564352035522},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6215882301330566},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49653512239456177},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3620122969150543},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3457966446876526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09146237373352051},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07585275173187256}],"concepts":[{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.9625427722930908},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8760912418365479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.742415189743042},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6684564352035522},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6215882301330566},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49653512239456177},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3620122969150543},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3457966446876526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09146237373352051},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07585275173187256},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms9020065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9020065","pdf_url":"https://www.mdpi.com/2075-1680/9/2/65/pdf?version=1593497733","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:06780603c1844651a735421eb5fc80c4","is_oa":true,"landing_page_url":"https://doaj.org/article/06780603c1844651a735421eb5fc80c4","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":"Axioms, Vol 9, Iss 2, p 65 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/9/2/65/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms9020065","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":"Axioms; Volume 9; Issue 2; Pages: 65","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms9020065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9020065","pdf_url":"https://www.mdpi.com/2075-1680/9/2/65/pdf?version=1593497733","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3032990393.pdf","grobid_xml":"https://content.openalex.org/works/W3032990393.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W96079624","https://openalex.org/W271810198","https://openalex.org/W1522419168","https://openalex.org/W1606297705","https://openalex.org/W1965955764","https://openalex.org/W1976039496","https://openalex.org/W1994123225","https://openalex.org/W2011083349","https://openalex.org/W2034038007","https://openalex.org/W2064294848","https://openalex.org/W2066397800","https://openalex.org/W2070514473","https://openalex.org/W2070545443","https://openalex.org/W2084088638","https://openalex.org/W2086830112","https://openalex.org/W2088404102","https://openalex.org/W2105640560","https://openalex.org/W2112815753","https://openalex.org/W2218791914","https://openalex.org/W2286842691","https://openalex.org/W2502556501","https://openalex.org/W2625006735","https://openalex.org/W2789840537","https://openalex.org/W2900734811","https://openalex.org/W2906368873","https://openalex.org/W2912565176","https://openalex.org/W2955560030","https://openalex.org/W4211007335","https://openalex.org/W4285719527","https://openalex.org/W6604011458","https://openalex.org/W6672205434","https://openalex.org/W6688964854","https://openalex.org/W6739620244"],"related_works":["https://openalex.org/W2373677839","https://openalex.org/W3032990393","https://openalex.org/W2766222296","https://openalex.org/W3011491025","https://openalex.org/W2234982114","https://openalex.org/W4252252919","https://openalex.org/W2952485748","https://openalex.org/W1540184672","https://openalex.org/W4299430380","https://openalex.org/W2249012960"],"abstract_inverted_index":{"This":[0],"paper":[1],"mainly":[2],"deals":[3],"with":[4,63],"introducing":[5],"and":[6],"studying":[7],"the":[8],"properties":[9],"of":[10,43],"generalized":[11,32,55],"nabla":[12,33,45,56],"differentiability":[13],"for":[14,31,48],"fuzzy":[15,35,49],"functions":[16,50],"on":[17,28,51],"time":[18,52],"scales":[19,53],"via":[20],"Hukuhara":[21],"difference.":[22],"Further,":[23],"we":[24,38],"obtain":[25],"embedding":[26],"results":[27,60],"E":[29],"n":[30],"differentiable":[34],"functions.":[36],"Finally,":[37],"prove":[39],"a":[40,44],"fundamental":[41],"theorem":[42],"integral":[46],"calculus":[47],"under":[54],"differentiability.":[57],"The":[58],"obtained":[59],"are":[61],"illustrated":[62],"suitable":[64],"examples.":[65]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
