{"title":"含Caputo-Fabrizio导数的分数阶微分方程初值问题解的唯一性","authors":"Shuqin Zhang, Lei Hu, Sujing Sun","doi":"10.22436/JNSA.011.03.11","DOIUrl":null,"url":null,"abstract":"In this paper, we study some results about the expression of solutions to some linear differential equations for the CaputoFabrizio fractional derivative. Furthermore, by the Banach contraction principle, the unique existence of the solution to an initial value problem for nonlinear differential equation involving the Caputo-Fabrizio fractional derivative is obtained.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"5 1","pages":"428-436"},"PeriodicalIF":0.0000,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The uniqueness of solution for initial value problems for fractional differential equation involving the Caputo-Fabrizio derivative\",\"authors\":\"Shuqin Zhang, Lei Hu, Sujing Sun\",\"doi\":\"10.22436/JNSA.011.03.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study some results about the expression of solutions to some linear differential equations for the CaputoFabrizio fractional derivative. Furthermore, by the Banach contraction principle, the unique existence of the solution to an initial value problem for nonlinear differential equation involving the Caputo-Fabrizio fractional derivative is obtained.\",\"PeriodicalId\":22770,\"journal\":{\"name\":\"The Journal of Nonlinear Sciences and Applications\",\"volume\":\"5 1\",\"pages\":\"428-436\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Nonlinear Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22436/JNSA.011.03.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/JNSA.011.03.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The uniqueness of solution for initial value problems for fractional differential equation involving the Caputo-Fabrizio derivative
In this paper, we study some results about the expression of solutions to some linear differential equations for the CaputoFabrizio fractional derivative. Furthermore, by the Banach contraction principle, the unique existence of the solution to an initial value problem for nonlinear differential equation involving the Caputo-Fabrizio fractional derivative is obtained.
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