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 :海南师范大学数学与统计学院,海南 海口; 任 洁 :黎安初级中学,海南 陵水;

关键词: 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

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。

Abstract: 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.

文章引用: 林诗游 , 任 洁 (2016) 一类分数阶微分方程解的性质探讨。 理论数学, 6, 56-64. doi: 10.12677/PM.2016.61009

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