{"title":"基于奇异核的新型冠状病毒模型分数阶数学模型的理论与数值分析","authors":"Pratibha Verma, Surabhi Tiwari, Akanksha Verma","doi":"10.1007/s40010-022-00805-9","DOIUrl":null,"url":null,"abstract":"<div><p>This study presents a fractional-order mathematical model of coronavirus. We select COVID-19 model and convert the model into fractional order. Discuss its theoretical and numerical analysis. Firstly, we investigate the existence and uniqueness results using some fixed point theorems for the proposed fractional-order COVID-19 model. Further, we provide the stability analysis with the help of the Hyers-Ulam stability. The fractional operator is used in the Caputo sense. We obtain numerical solutions using famous numerical methods and provide a graphical interpretation using adopted numerical methods. Finally, we compare the above techniques and provide observations according to the obtained solutions.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"93 2","pages":"219 - 232"},"PeriodicalIF":0.8000,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Theoretical and Numerical Analysis of Fractional Order Mathematical Model on Recent COVID-19 Model Using Singular Kernel\",\"authors\":\"Pratibha Verma, Surabhi Tiwari, Akanksha Verma\",\"doi\":\"10.1007/s40010-022-00805-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This study presents a fractional-order mathematical model of coronavirus. We select COVID-19 model and convert the model into fractional order. Discuss its theoretical and numerical analysis. Firstly, we investigate the existence and uniqueness results using some fixed point theorems for the proposed fractional-order COVID-19 model. Further, we provide the stability analysis with the help of the Hyers-Ulam stability. The fractional operator is used in the Caputo sense. We obtain numerical solutions using famous numerical methods and provide a graphical interpretation using adopted numerical methods. Finally, we compare the above techniques and provide observations according to the obtained solutions.</p></div>\",\"PeriodicalId\":744,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"volume\":\"93 2\",\"pages\":\"219 - 232\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-01-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40010-022-00805-9\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-022-00805-9","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Theoretical and Numerical Analysis of Fractional Order Mathematical Model on Recent COVID-19 Model Using Singular Kernel
This study presents a fractional-order mathematical model of coronavirus. We select COVID-19 model and convert the model into fractional order. Discuss its theoretical and numerical analysis. Firstly, we investigate the existence and uniqueness results using some fixed point theorems for the proposed fractional-order COVID-19 model. Further, we provide the stability analysis with the help of the Hyers-Ulam stability. The fractional operator is used in the Caputo sense. We obtain numerical solutions using famous numerical methods and provide a graphical interpretation using adopted numerical methods. Finally, we compare the above techniques and provide observations according to the obtained solutions.
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