{"id":"https://openalex.org/W4317608847","doi":"https://doi.org/10.3390/sym15020286","title":"Analysis of the Mathematical Modelling of COVID-19 by Using Mild Solution with Delay Caputo Operator","display_name":"Analysis of the Mathematical Modelling of COVID-19 by Using Mild Solution with Delay Caputo Operator","publication_year":2023,"publication_date":"2023-01-19","ids":{"openalex":"https://openalex.org/W4317608847","doi":"https://doi.org/10.3390/sym15020286"},"language":"en","primary_location":{"id":"doi:10.3390/sym15020286","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020286","pdf_url":"https://www.mdpi.com/2073-8994/15/2/286/pdf?version=1675072407","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/2073-8994/15/2/286/pdf?version=1675072407","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076378258","display_name":"Kinda Abuasbeh","orcid":"https://orcid.org/0000-0003-2744-6320"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Kinda Abuasbeh","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-2744-6320","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016185347","display_name":"Ramsha Shafqat","orcid":"https://orcid.org/0000-0002-3610-339X"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]},{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Ramsha Shafqat","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3610-339X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435","https://openalex.org/I142204992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090640086","display_name":"Ammar Alsinai","orcid":"https://orcid.org/0000-0002-5221-0574"},"institutions":[{"id":"https://openalex.org/I204743663","display_name":"University of Mysore","ror":"https://ror.org/012bxv356","country_code":"IN","type":"education","lineage":["https://openalex.org/I204743663"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ammar Alsinai","raw_affiliation_strings":["Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570006, India"],"raw_orcid":"https://orcid.org/0000-0002-5221-0574","affiliations":[{"raw_affiliation_string":"Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570006, India","institution_ids":["https://openalex.org/I204743663"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060006810","display_name":"Muath Awadalla","orcid":"https://orcid.org/0000-0002-6447-6361"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muath Awadalla","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-6447-6361","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016185347","https://openalex.org/A5076378258","https://openalex.org/A5090640086"],"corresponding_institution_ids":["https://openalex.org/I142204992","https://openalex.org/I160968435","https://openalex.org/I204743663","https://openalex.org/I4626487"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.9596,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.94012471,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"15","issue":"2","first_page":"286","last_page":"286"},"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":0.9900000095367432,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9873999953269958,"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/uniqueness","display_name":"Uniqueness","score":0.7793945074081421},{"id":"https://openalex.org/keywords/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.7688716650009155},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7029776573181152},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6520869731903076},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6135882139205933},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6052516102790833},{"id":"https://openalex.org/keywords/coronavirus-disease-2019","display_name":"Coronavirus disease 2019 (COVID-19)","score":0.5744287967681885},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5267224311828613},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.48473331332206726},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.44657814502716064},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.439674973487854},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4216650724411011},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33725088834762573},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31086844205856323},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1830618977546692},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.0654776394367218}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7793945074081421},{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.7688716650009155},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7029776573181152},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6520869731903076},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6135882139205933},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6052516102790833},{"id":"https://openalex.org/C3008058167","wikidata":"https://www.wikidata.org/wiki/Q84263196","display_name":"Coronavirus disease 2019 (COVID-19)","level":4,"score":0.5744287967681885},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5267224311828613},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.48473331332206726},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.44657814502716064},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.439674973487854},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4216650724411011},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33725088834762573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31086844205856323},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1830618977546692},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0654776394367218},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C524204448","wikidata":"https://www.wikidata.org/wiki/Q788926","display_name":"Infectious disease (medical specialty)","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15020286","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020286","pdf_url":"https://www.mdpi.com/2073-8994/15/2/286/pdf?version=1675072407","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:fa796d949a38431bb0ff5f6c1dbb67ac","is_oa":false,"landing_page_url":"https://doaj.org/article/fa796d949a38431bb0ff5f6c1dbb67ac","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 2, p 286 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/2/286/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15020286","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15020286","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020286","pdf_url":"https://www.mdpi.com/2073-8994/15/2/286/pdf?version=1675072407","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331156","display_name":"King Faisal University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4317608847.pdf","grobid_xml":"https://content.openalex.org/works/W4317608847.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W43498744","https://openalex.org/W1996607325","https://openalex.org/W1997441517","https://openalex.org/W2069565238","https://openalex.org/W2556784265","https://openalex.org/W2740460687","https://openalex.org/W2780541558","https://openalex.org/W2787959293","https://openalex.org/W2922726777","https://openalex.org/W2944615032","https://openalex.org/W2944890452","https://openalex.org/W2946851523","https://openalex.org/W3004912618","https://openalex.org/W3007784796","https://openalex.org/W3011134403","https://openalex.org/W3014205176","https://openalex.org/W3031209935","https://openalex.org/W3032512614","https://openalex.org/W3039119913","https://openalex.org/W3087667739","https://openalex.org/W3090595831","https://openalex.org/W3092410253","https://openalex.org/W3093441489","https://openalex.org/W3108227513","https://openalex.org/W3111152365","https://openalex.org/W3113679393","https://openalex.org/W3129313820","https://openalex.org/W3170389675","https://openalex.org/W3180973001","https://openalex.org/W3189224876","https://openalex.org/W4200599879","https://openalex.org/W4210532615","https://openalex.org/W4210577689","https://openalex.org/W4282921778","https://openalex.org/W4283640579","https://openalex.org/W4294081519","https://openalex.org/W4294636927","https://openalex.org/W4296351246","https://openalex.org/W4297105184","https://openalex.org/W4311447043","https://openalex.org/W4311862179","https://openalex.org/W4400466286","https://openalex.org/W6601779485","https://openalex.org/W6730176618","https://openalex.org/W6748396876","https://openalex.org/W6786650610","https://openalex.org/W6842982142","https://openalex.org/W6843213130"],"related_works":["https://openalex.org/W4313233315","https://openalex.org/W3095724723","https://openalex.org/W1586145079","https://openalex.org/W4401383466","https://openalex.org/W4281619695","https://openalex.org/W2901432230","https://openalex.org/W2048436983","https://openalex.org/W2233017382","https://openalex.org/W2523462812","https://openalex.org/W4317627639"],"abstract_inverted_index":{"This":[0],"work":[1],"investigates":[2],"a":[3,13],"mathematical":[4],"fractional-order":[5],"model":[6,47,97],"that":[7,51,76,93],"depicts":[8],"the":[9,19,24,28,34,42,66,69,73,82,89,94],"Caputo":[10],"growth":[11],"of":[12,23,45,56,68],"new":[14,70,90],"coronavirus":[15,96],"(COVID-19).":[16],"We":[17],"studied":[18],"existence":[20],"and":[21,48,72],"uniqueness":[22],"linked":[25],"solution":[26,44],"using":[27],"fixed":[29],"point":[30],"theory":[31],"method.":[32],"Using":[33],"Laplace":[35],"Adomian":[36],"decomposition":[37],"method":[38],"(LADM),":[39],"we":[40,77],"explored":[41],"precise":[43],"our":[46,86],"obtained":[49],"results":[50,87],"are":[52],"stated":[53],"in":[54],"terms":[55],"infinite":[57],"series.":[58],"Numerical":[59],"data":[60],"were":[61],"then":[62],"used":[63],"to":[64,81],"demonstrate":[65],"use":[67],"derivative":[71],"symmetric":[74],"structure":[75],"created.":[78],"When":[79],"compared":[80],"traditional":[83],"order":[84],"derivatives,":[85],"under":[88],"hypothesis":[91],"show":[92],"innovative":[95],"performs":[98],"better.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2025-10-10T00:00:00"}