{"title":"非线性偏分数阶微分方程的近似解","authors":"K. Gepreel, T. Nofal","doi":"10.15866/IREPHY.V7I4.4444","DOIUrl":null,"url":null,"abstract":"In this article, we use the Adomain decomposition method to find the approximate solutions for the linear and nonlinear partial fractional differential equations via the nonlinear Schrodinger partial fractional differential equation and the telegraph partial fractional differential equation. The fractional derivatives are described in the Caputo sense. We compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. Also we make the Figures to compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. This method is powerfull to find the approximate solutions for nonlinear partial fractional differential equations. Also we will compare between the approximate solutions which obtained by using the variational itearation method and the approximate solutions which obtained by Adomain decomposition methods.","PeriodicalId":448231,"journal":{"name":"International Review of Physics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximate Solutions for Nonlinear Partial Fractional Differential Equations\",\"authors\":\"K. Gepreel, T. Nofal\",\"doi\":\"10.15866/IREPHY.V7I4.4444\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we use the Adomain decomposition method to find the approximate solutions for the linear and nonlinear partial fractional differential equations via the nonlinear Schrodinger partial fractional differential equation and the telegraph partial fractional differential equation. The fractional derivatives are described in the Caputo sense. We compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. Also we make the Figures to compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. This method is powerfull to find the approximate solutions for nonlinear partial fractional differential equations. Also we will compare between the approximate solutions which obtained by using the variational itearation method and the approximate solutions which obtained by Adomain decomposition methods.\",\"PeriodicalId\":448231,\"journal\":{\"name\":\"International Review of Physics\",\"volume\":\"39 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-08-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Review of Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15866/IREPHY.V7I4.4444\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Review of Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15866/IREPHY.V7I4.4444","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximate Solutions for Nonlinear Partial Fractional Differential Equations
In this article, we use the Adomain decomposition method to find the approximate solutions for the linear and nonlinear partial fractional differential equations via the nonlinear Schrodinger partial fractional differential equation and the telegraph partial fractional differential equation. The fractional derivatives are described in the Caputo sense. We compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. Also we make the Figures to compare between the approximate solutions and the exact solutions for the partial fractional differential equations when α,β→1. This method is powerfull to find the approximate solutions for nonlinear partial fractional differential equations. Also we will compare between the approximate solutions which obtained by using the variational itearation method and the approximate solutions which obtained by Adomain decomposition methods.