{"id":"https://openalex.org/W1903750877","doi":"https://doi.org/10.1016/j.jksus.2015.08.001","title":"Existence and uniqueness of solution for a fractional Riemann\u2013Liouville initial value problem on time scales","display_name":"Existence and uniqueness of solution for a fractional Riemann\u2013Liouville initial value problem on time scales","publication_year":2015,"publication_date":"2015-08-11","ids":{"openalex":"https://openalex.org/W1903750877","doi":"https://doi.org/10.1016/j.jksus.2015.08.001","mag":"1903750877"},"language":"en","primary_location":{"id":"doi:10.1016/j.jksus.2015.08.001","doi":"https://doi.org/10.1016/j.jksus.2015.08.001","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jksus.2015.08.001","pdf_url":null,"source":{"id":"https://openalex.org/S163784168","display_name":"Journal of King Saud University - Science","issn_l":"1018-3647","issn":["1018-3647","2213-686X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1","poland-70","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of King Saud University - Science","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.jksus.2015.08.001","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011940046","display_name":"Nadia Benkhettou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210125514","display_name":"Universit\u00e9 Djilali de Sidi Bel Abb\u00e8s","ror":"https://ror.org/0378szg41","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210125514"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Nadia Benkhettou","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques, Universit\u00e9 de Sidi Bel-Abb\u00e8s, B.P. 89, 22000 Sidi Bel-Abb\u00e8s, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques, Universit\u00e9 de Sidi Bel-Abb\u00e8s, B.P. 89, 22000 Sidi Bel-Abb\u00e8s, Algeria","institution_ids":["https://openalex.org/I4210125514"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045726899","display_name":"Ahmed Hammoudi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210163438","display_name":"Universit\u00e9 de ain T\u00e9mouchent","ror":"https://ror.org/05ckyqt97","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210163438"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Ahmed Hammoudi","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques, Universit\u00e9 de Ain T\u00e9mouchentl, B.P. 89, 46000 Ain T\u00e9mouchent, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques, Universit\u00e9 de Ain T\u00e9mouchentl, B.P. 89, 46000 Ain T\u00e9mouchent, Algeria","institution_ids":["https://openalex.org/I4210163438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057131265","display_name":"Delfim F. M. Torres","orcid":"https://orcid.org/0000-0001-8641-2505","observed_orcids":["https://orcid.org/0000-0001-8641-2505"]},"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":true,"raw_author_name":"Delfim F.M. Torres","raw_affiliation_strings":["Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057131265"],"corresponding_institution_ids":["https://openalex.org/I60858718"],"apc_list":{"value":1600,"currency":"USD","value_usd":1600},"apc_paid":{"value":1600,"currency":"USD","value_usd":1600},"fwci":6.9826,"has_fulltext":true,"cited_by_count":59,"citation_normalized_percentile":{"value":0.97683308,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"28","issue":"1","first_page":"87","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9932000041007996,"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":0.9932000041007996,"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":0.004399999976158142,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.001500000013038516,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/riemann-liouville-fractional-derivative","display_name":"Riemann-Liouville fractional derivative","score":0.9649999737739563},{"id":"https://openalex.org/keywords/timescales","display_name":"time scales","score":0.9380000233650208},{"id":"https://openalex.org/keywords/fractional-initial-value-problems","display_name":"fractional initial value problems","score":0.7820000052452087},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.8349999785423279},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.9869999885559082}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8679999709129333},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.7748000025749207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7699999809265137},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5688999891281128},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5012000203132629},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4936999976634979},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4672999978065491},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.44510000944137573},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C98724732","wikidata":"https://www.wikidata.org/wiki/Q1935235","display_name":"Mittag-Leffler function","level":3,"score":0.3084000051021576},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2572999894618988}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1016/j.jksus.2015.08.001","doi":"https://doi.org/10.1016/j.jksus.2015.08.001","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jksus.2015.08.001","pdf_url":null,"source":{"id":"https://openalex.org/S163784168","display_name":"Journal of King Saud University - Science","issn_l":"1018-3647","issn":["1018-3647","2213-686X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1","poland-70","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of King Saud University - Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1508.00754","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.00754","pdf_url":"https://arxiv.org/pdf/1508.00754","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:doaj.org/article:d746d8fee1f74fa685fb78da4f87ff19","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/d746d8fee1f74fa685fb78da4f87ff19","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,"listed_in":[],"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":"Journal of King Saud University: Science, Vol 28, Iss 1, Pp 87-92 (2016)","raw_type":"article"},{"id":"pmh:oai:ria.ua.pt:10773/16633","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10773/16633","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},{"id":"doi:10.48550/arxiv.1508.00754","doi":"https://doi.org/10.48550/arxiv.1508.00754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1508.00754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1016/j.jksus.2015.08.001","doi":"https://doi.org/10.1016/j.jksus.2015.08.001","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jksus.2015.08.001","pdf_url":null,"source":{"id":"https://openalex.org/S163784168","display_name":"Journal of King Saud University - Science","issn_l":"1018-3647","issn":["1018-3647","2213-686X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1","poland-70","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of King Saud University - Science","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1607522747","display_name":"Centro de Investiga\u00e7\u00e3o e Desenvolvimento em Matem\u00e1tica e Aplica\u00e7\u00f5es","funder_award_id":"UID/MAT/04106/2013","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3069120617","display_name":null,"funder_award_id":"04106","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G396988802","display_name":null,"funder_award_id":"UID/MAT/04106/2013","funder_id":"https://openalex.org/F4320310000","funder_display_name":"Universidade de Aveiro"},{"id":"https://openalex.org/G6751613957","display_name":null,"funder_award_id":"UID/MAT/04106/2013","funder_id":"https://openalex.org/F4320329951","funder_display_name":"Center for Research and Development in Mathematics and Applications"}],"funders":[{"id":"https://openalex.org/F4320310000","display_name":"Universidade de Aveiro","ror":"https://ror.org/00nt41z93"},{"id":"https://openalex.org/F4320329951","display_name":"Center for Research and Development in Mathematics and Applications","ror":null},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1903750877.pdf","grobid_xml":"https://content.openalex.org/works/W1903750877.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W271810198","https://openalex.org/W304963343","https://openalex.org/W1522419168","https://openalex.org/W1904514963","https://openalex.org/W1918125490","https://openalex.org/W1963783436","https://openalex.org/W2070514473","https://openalex.org/W2092444463","https://openalex.org/W2137369682","https://openalex.org/W2748999637","https://openalex.org/W3020894078","https://openalex.org/W3103316083","https://openalex.org/W6640365429"],"related_works":["https://openalex.org/W4386829715","https://openalex.org/W3155770204","https://openalex.org/W2795638701","https://openalex.org/W7217634407","https://openalex.org/W4291638219","https://openalex.org/W1918125490","https://openalex.org/W4242036608","https://openalex.org/W4364374057","https://openalex.org/W4322718569","https://openalex.org/W2162307620"],"abstract_inverted_index":{"We":[0],"introduce":[1],"the":[2,15],"concept":[3],"of":[4,7,14],"fractional":[5,30],"derivative":[6],"Riemann\u2013Liouville":[8],"on":[9,34],"time":[10,37],"scales.":[11],"Fundamental":[12],"properties":[13],"new":[16],"operator":[17],"are":[18],"proved,":[19],"as":[20,22],"well":[21],"an":[23,35],"existence":[24],"and":[25],"uniqueness":[26],"result":[27],"for":[28],"a":[29],"initial":[31],"value":[32],"problem":[33],"arbitrary":[36],"scale.":[38]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}