%0 Journal Article
%T 一类分数阶微分方程解的性质探讨<br>Exploration on the Nature of Solutions for a Differential Equation of Fractional Order
%A 林诗游
%A 任洁
%J Pure Mathematics
%P 56-64
%@ 2160-7605
%D 2016
%I Hans Publishing
%R 10.12677/PM.2016.61009
%X <div style=\"text-align:justify;\">
	<span style=\"line-height:1.5;\">本文主要证明了一类分数阶非线性微分方程解的存在性和唯一性。文中用到的微分算子是Caputo分数阶微分算子。因这类方程的可解性是与一类Volterra型的积分方程的可解性等价，所以我们主要研究了与之等价的积分方程解的存在性和唯一性。我们通过Schauder不动点定理证明了积分方程解的存在性，用压缩映象原理证明了解的唯一性。<br />
We prove existence and uniqueness of the solution of a nonlinear differential equation of fractional order. The differential operator is the Caputo fractional derivative. For the solvability of the equation is equivalent to a class of Volterra integral equation, we study the existence and uniqueness of the integral equation. We prove the existence of the solution of integral equation by Schau- der fixed point theorem and the uniqueness of the solution by contraction mapping principle.</span><span style=\"line-height:1.5;\"></span> 
</div>
%K 分数阶微分方程，Caputo微分，Schauder不动点定理，压缩映象原理<br>Differential Equation of Fractional Order
%K Caputo Derivative
%K Schauder Fixed Point Theorem
%K Contraction Mapping Principle
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=16854