标题:
一类分数阶微分方程解的性质探讨Exploration on the Nature of Solutions for a Differential Equation of Fractional Order
作者:
林诗游, 任洁
关键字:
分数阶微分方程, Caputo微分, Schauder不动点定理, 压缩映象原理Differential Equation of Fractional Order, Caputo Derivative, Schauder Fixed Point Theorem, Contraction Mapping Principle
期刊名称:
《Pure Mathematics》, Vol.6 No.1, 2016-01-29
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。
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.