Existence and uniqueness for a class of multi-term fractional differential equations

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• 作者：Qiuping Li ; Chuanxia Hou ; Liying Sun…
• 关键词：Fractional differential equation ; Initial value problem ; Existence ; Uniqueness ; Schauder fixed point theorem ; Banach contraction principle
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：383-395
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

In this paper, we consider the initial value problem for the nonlinear fractional differential equations $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} D^\alpha u(t)=f(t,u(t),D^{\beta _1}u(t),\ldots ,D^{\beta _N}u(t)), \quad &{}t\in (0,1],\\ D^{\alpha -k}u(0)=0, \quad &{}k=1,2,\ldots ,n, \end{array} \right. \end{aligned}$$where \(\alpha >\beta _1>\beta _2>\cdots \beta _N>0\), \(n=[\alpha ]+1\) for \(\alpha \notin \mathbb {N}\) and \(\alpha =n\) for \(\alpha \in \mathbb {N}\), \(\beta _j<1\) for any \(j\in \{1,2,\ldots ,N\}\), D is the standard Riemann–Liouville derivative and \(f:[0,1]\times \mathbb {R}^{N+1}\rightarrow \mathbb {R}\) is a given function. By means of Schauder fixed point theorem and Banach contraction principle, an existence result and a unique result for the solution are obtained,respectively. 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Comput. 257, 526–536 (2015)MathSciNetMATHGoogle ScholarCopyright information© Korean Society for Computational and Applied Mathematics 2015Authors and AffiliationsQiuping Li12Chuanxia Hou1Liying Sun1Zhenlai Han1Email author1.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China2.Quancheng CollegeUniversity of JinanPenglaiPeople’s Republic of China About this article CrossMark Publisher Name Springer Berlin Heidelberg Print ISSN 1598-5865 Online ISSN 1865-2085 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; background-color: #f2f2f2; 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