一类分数阶微分方程解的性质探讨.pdf

Pure Mathematics 理论数学, 2016, 6(1), 56-64 Published Online January 2016 in Hans. /journal/pm /10.12677/pm.2016.61009 Exploration on the Nature of Solutions for a Differential Equation of Fractional Order 1 2 Shiyou Lin , Jie Ren 1 School of Mathematics and Statistics, Hainan Normal University, Haikou Hainan 2 Li’an Junior High School, Lingshui Hainan th th th Received: Dec. 30 , 2015; accepted: Jan. 24 , 2016; published: Jan. 29 , 2016 Copyright © 2016 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract We prove existence and uniqueness of the solution of a nonlinear differential equation of fraction- al 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 unique- ness 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. Keywords Differential Equation of Fractional Order, Caputo Derivative, Schauder Fixed Point Theorem, Contraction Mapping Principle 一类分数阶微分方程解的性质探讨 1 2 林诗游 ，任 洁 1海南师范大学数学与统计学院，海南 海口 2黎安初级中学，海南 陵水 收稿日期：2015年12月30 日；录用日期：2016年1月24 日；发布日期：2016年1月29 日 文章引用: 林诗游, 任洁. 一类分数阶微分方程解的性质探讨[J]. 理论数学, 2016, 6(1): 56-64. /10.12677/pm.2016.61009 林诗游，任洁 摘 要 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