{"id":"https://openalex.org/W3126261180","doi":"https://doi.org/10.1142/s1793962321500379","title":"A mathematical study of a tuberculosis model with fractional derivatives","display_name":"A mathematical study of a tuberculosis model with fractional derivatives","publication_year":2021,"publication_date":"2021-02-04","ids":{"openalex":"https://openalex.org/W3126261180","doi":"https://doi.org/10.1142/s1793962321500379","mag":"3126261180"},"language":"en","primary_location":{"id":"doi:10.1142/s1793962321500379","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962321500379","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","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/A5000389041","display_name":"Hamadjam Abboubakar","orcid":"https://orcid.org/0000-0002-2213-7185"},"institutions":[{"id":"https://openalex.org/I59196294","display_name":"University of Ngaound\u00e9r\u00e9","ror":"https://ror.org/03gq1d339","country_code":"CM","type":"education","lineage":["https://openalex.org/I59196294"]}],"countries":["CM"],"is_corresponding":true,"raw_author_name":"Hamadjam Abboubakar","raw_affiliation_strings":["Department of Computer Engineering, University Institute of Technology, University of Ngaound\u00e9r\u00e9, P.O. Box 455, Ngaound\u00e9r\u00e9, Cameroon"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, University Institute of Technology, University of Ngaound\u00e9r\u00e9, P.O. Box 455, Ngaound\u00e9r\u00e9, Cameroon","institution_ids":["https://openalex.org/I59196294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031475130","display_name":"Pushpendra Kumar","orcid":"https://orcid.org/0000-0002-7755-2837"},"institutions":[{"id":"https://openalex.org/I114724429","display_name":"Central University of Punjab","ror":"https://ror.org/02kknsa06","country_code":"IN","type":"education","lineage":["https://openalex.org/I114724429"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pushpendra Kumar","raw_affiliation_strings":["Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab-151001, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab-151001, India","institution_ids":["https://openalex.org/I114724429"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090029811","display_name":"Vedat Suat Ert\u00fcrk","orcid":"https://orcid.org/0000-0002-1322-8843"},"institutions":[{"id":"https://openalex.org/I227306068","display_name":"Ondokuz May\u0131s University","ror":"https://ror.org/028k5qw24","country_code":"TR","type":"education","lineage":["https://openalex.org/I227306068"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Vedat Suat Erturk","raw_affiliation_strings":["Department of Mathematics, Ondokuz Mayis University, Atakum-55200, Samsun, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ondokuz Mayis University, Atakum-55200, Samsun, Turkey","institution_ids":["https://openalex.org/I227306068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051902290","display_name":"Anoop Kumar","orcid":"https://orcid.org/0000-0003-4514-4449"},"institutions":[{"id":"https://openalex.org/I114724429","display_name":"Central University of Punjab","ror":"https://ror.org/02kknsa06","country_code":"IN","type":"education","lineage":["https://openalex.org/I114724429"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anoop Kumar","raw_affiliation_strings":["Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab-151001, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab-151001, India","institution_ids":["https://openalex.org/I114724429"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000389041"],"corresponding_institution_ids":["https://openalex.org/I59196294"],"apc_list":null,"apc_paid":null,"fwci":3.5828,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.93720737,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"12","issue":"04","first_page":"2150037","last_page":"2150037"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/fractional-calculus","display_name":"Fractional calculus","score":0.8369008898735046},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.745466947555542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7088152170181274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6527981758117676},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6253666281700134},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5582752227783203},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5134137868881226},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4706045091152191},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2424640953540802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18082979321479797}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.8369008898735046},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.745466947555542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7088152170181274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6527981758117676},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6253666281700134},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5582752227783203},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5134137868881226},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4706045091152191},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2424640953540802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18082979321479797},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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:10.1142/s1793962321500379","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962321500379","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W753712656","https://openalex.org/W1105047175","https://openalex.org/W1542917443","https://openalex.org/W2005274550","https://openalex.org/W2031306648","https://openalex.org/W2097614441","https://openalex.org/W2114485289","https://openalex.org/W2265417715","https://openalex.org/W2315281247","https://openalex.org/W2460141082","https://openalex.org/W2493299873","https://openalex.org/W2752547294","https://openalex.org/W2763033987","https://openalex.org/W2773396578","https://openalex.org/W2784880924","https://openalex.org/W2790268520","https://openalex.org/W2791997229","https://openalex.org/W2894443826","https://openalex.org/W2899160818","https://openalex.org/W2916376709","https://openalex.org/W2917120690","https://openalex.org/W2945315710","https://openalex.org/W2963010124","https://openalex.org/W2965430512","https://openalex.org/W2995168318","https://openalex.org/W3020522035","https://openalex.org/W3035206308","https://openalex.org/W3087529349","https://openalex.org/W3087549304","https://openalex.org/W3094549672","https://openalex.org/W3097095656","https://openalex.org/W3099147493","https://openalex.org/W4237878614","https://openalex.org/W4253062931"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2089892488","https://openalex.org/W2416906960","https://openalex.org/W2050580331"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,60,103],"use":[4],"a":[5,127],"Predictor\u2013Corrector":[6,97],"method":[7],"to":[8,117],"implement":[9],"and":[10,29,52,82,136],"derive":[11],"an":[12,16],"iterative":[13,87],"solution":[14,88],"of":[15,56,66,69,84,89,110],"existing":[17,41],"Tuberculosis":[18],"(TB)":[19],"model":[20],"with":[21],"two":[22,91],"fractional":[23,27,34,71,78,112,124,134],"derivatives,":[24],"namely,":[25],"Caputo\u2013Fabrizio":[26,133],"derivative":[28,125,135],"the":[30,45,53,57,62,70,80,90,96,111,120,132,137],"new":[31,121],"generalized":[32,122],"Caputo":[33,123],"derivative.":[35],"We":[36,73],"begin":[37],"by":[38],"recalling":[39],"some":[40],"results":[42,115],"such":[43],"as":[44],"basic":[46],"reproduction":[47],"number":[48],"[Formula:":[49],"see":[50],"text]":[51],"equilibrium":[54,68],"points":[55],"model.":[58,141],"Then,":[59],"study":[61],"global":[63],"asymptotic":[64],"stability":[65],"disease-free":[67],"models.":[72],"also":[74],"prove,":[75],"for":[76,107],"each":[77],"model,":[79],"existence":[81],"uniqueness":[83],"solutions.":[85],"An":[86],"models":[92],"is":[93],"computed":[94],"using":[95],"method.":[98],"Using":[99],"realistic":[100,129],"parameter":[101],"values,":[102],"perform":[104],"numerical":[105],"simulations":[106],"different":[108],"values":[109],"order.":[113],"Simulation":[114],"permit":[116],"conclude":[118],"that":[119],"provides":[126],"more":[128],"analysis":[130],"than":[131],"classical":[138],"integer-order":[139],"TB":[140]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":19}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
