{"id":"https://openalex.org/W2605374304","doi":"https://doi.org/10.3233/fi-2017-1494","title":"A New Approach for Modeling with Discrete Fractional Equations","display_name":"A New Approach for Modeling with Discrete Fractional Equations","publication_year":2017,"publication_date":"2017-03-11","ids":{"openalex":"https://openalex.org/W2605374304","doi":"https://doi.org/10.3233/fi-2017-1494","mag":"2605374304"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2017-1494","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2017-1494","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"type":"article","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/A5061185771","display_name":"Ferhan M. At\u0131c\u0131","orcid":"https://orcid.org/0000-0002-9862-9901"},"institutions":[{"id":"https://openalex.org/I94339441","display_name":"Western Kentucky University","ror":"https://ror.org/0446vnd56","country_code":"US","type":"education","lineage":["https://openalex.org/I94339441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ferhan M. At\u0131c\u0131","raw_affiliation_strings":["Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA. ferhan.atici@wku.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA. ferhan.atici@wku.edu","institution_ids":["https://openalex.org/I94339441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030446247","display_name":"Mustafa At\u0131c\u0131","orcid":null},"institutions":[{"id":"https://openalex.org/I94339441","display_name":"Western Kentucky University","ror":"https://ror.org/0446vnd56","country_code":"US","type":"education","lineage":["https://openalex.org/I94339441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mustafa At\u0131c\u0131","raw_affiliation_strings":["Department of Computer Science, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA. mustafa.atici@wku.edu"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA. mustafa.atici@wku.edu","institution_ids":["https://openalex.org/I94339441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088570437","display_name":"Michael Belcher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Belcher","raw_affiliation_strings":["Gatton Academy of Science and Mathematics, Bowling Green, Kentucky 42101 USA. michael.belcher403@topper.wku.edu"],"affiliations":[{"raw_affiliation_string":"Gatton Academy of Science and Mathematics, Bowling Green, Kentucky 42101 USA. michael.belcher403@topper.wku.edu","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026281396","display_name":"Dana Marshall","orcid":null},"institutions":[{"id":"https://openalex.org/I118073183","display_name":"Meharry Medical College","ror":"https://ror.org/00k63dq23","country_code":"US","type":"education","lineage":["https://openalex.org/I118073183"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dana Marshall","raw_affiliation_strings":["Department of Pathology, Anatomy and Cell Biology, Meharry Medical College, Nashville, Tennessee 37208 USA. dmarshall@mmc.edu"],"affiliations":[{"raw_affiliation_string":"Department of Pathology, Anatomy and Cell Biology, Meharry Medical College, Nashville, Tennessee 37208 USA. dmarshall@mmc.edu","institution_ids":["https://openalex.org/I118073183"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061185771"],"corresponding_institution_ids":["https://openalex.org/I94339441"],"apc_list":null,"apc_paid":null,"fwci":1.2323,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.7789122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"151","issue":"1-4","first_page":"313","last_page":"324"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991000294685364,"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":0.9991000294685364,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9768999814987183,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9379000067710876,"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/class","display_name":"Class (philosophy)","score":0.6060408353805542},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5945314764976501},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.590180516242981},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.53394615650177},{"id":"https://openalex.org/keywords/discrete-modelling","display_name":"Discrete modelling","score":0.4337245225906372},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4174908697605133},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33636343479156494},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29597797989845276},{"id":"https://openalex.org/keywords/discrete-system","display_name":"Discrete system","score":0.1904022991657257},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12075820565223694},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0669948160648346}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6060408353805542},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5945314764976501},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.590180516242981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.53394615650177},{"id":"https://openalex.org/C81146285","wikidata":"https://www.wikidata.org/wiki/Q5282053","display_name":"Discrete modelling","level":3,"score":0.4337245225906372},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4174908697605133},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33636343479156494},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29597797989845276},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.1904022991657257},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12075820565223694},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0669948160648346},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2017-1494","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2017-1494","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W2382250648","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158","https://openalex.org/W4379507409","https://openalex.org/W2561874146","https://openalex.org/W2066331732","https://openalex.org/W2291295292"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,25],"introduce":[4],"a":[5,27],"new":[6,28],"class":[7],"of":[8,38,51],"nonlinear":[9],"discrete":[10],"fractional":[11],"equations":[12],"to":[13],"model":[14],"tumor":[15],"growth":[16],"rates":[17],"in":[18],"mice.":[19],"For":[20],"the":[21,39,48,55],"data":[22],"fitting":[23],"purpose,":[24],"develop":[26],"method":[29,42],"which":[30],"can":[31],"be":[32],"considered":[33],"as":[34],"an":[35],"improved":[36],"version":[37],"partial":[40],"sum":[41],"for":[43],"parameter":[44],"estimations.":[45],"We":[46],"demonstrate":[47],"goodne":[49],"ss":[50],"fit":[52],"by":[53],"comparing":[54],"models":[56],"with":[57],"three":[58],"statistical":[59],"measures.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}