{"title":"线性和非线性分数阶微分方程的解析解","authors":"E. Ziada","doi":"10.21608/njbs.2021.202511","DOIUrl":null,"url":null,"abstract":"In this paper, we apply the Adomian decomposition method (ADM) for solving linear and nonlinear fractional differential equations (FDEs). The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are discussed. Some applications are solved such as relaxation-oscillation equation, Basset problem and fractional Riccati differential equation.","PeriodicalId":210317,"journal":{"name":"Nile Journal of Basic Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Analytical solution of linear and nonlinear fractional differential equations\",\"authors\":\"E. Ziada\",\"doi\":\"10.21608/njbs.2021.202511\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we apply the Adomian decomposition method (ADM) for solving linear and nonlinear fractional differential equations (FDEs). The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are discussed. Some applications are solved such as relaxation-oscillation equation, Basset problem and fractional Riccati differential equation.\",\"PeriodicalId\":210317,\"journal\":{\"name\":\"Nile Journal of Basic Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nile Journal of Basic Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21608/njbs.2021.202511\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nile Journal of Basic Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21608/njbs.2021.202511","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Analytical solution of linear and nonlinear fractional differential equations
In this paper, we apply the Adomian decomposition method (ADM) for solving linear and nonlinear fractional differential equations (FDEs). The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are discussed. Some applications are solved such as relaxation-oscillation equation, Basset problem and fractional Riccati differential equation.