上海交通大学学报

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (07): 1091-1094.

• 数学 • 上一篇    

一类分数阶非线性微分方程正解的存在性与唯一性

李晓艳，蒋威   

  1. (安徽大学 数学科学学院，安徽 合肥 230601)
  • 收稿日期:2010-04-06 出版日期:2011-07-29 发布日期:2011-07-29
  • 基金资助:

    国家自然科学基金资助项目（11071001），国家博士点基金项目（20093401110001），安徽省高校重大项目（KJ2010ZD02）

Existence and Uniqueness of Positive Solutions of a Class of Nonlinear Differential Equations of Fractional Order

 LI  Xiao-Yan, JIANG  Wei   

  • Received:2010-04-06 Online:2011-07-29 Published:2011-07-29

摘要：  利用巴拿赫空间锥上的不动点定理和压缩映像原理，研究了一类分数阶非线性微分方程正解的存在性与唯一性. 这类微分方程等号右边的非线性函数项中含有未知函数的分数阶导数.在给出这类微分方程解的积分表达式的基础上，分别得到了其正解存在和唯一的充分条件.文中还给出了2个例子来验证主要结果.

关键词: 分数阶微分方程, Caputo 导数, 正解

Abstract: By using the fixed point theorem and contraction mapping principle on a  cone in a real Banach space, the existence and uniqueness of positive solutions of nonlinear fractional differential equations in which the inhomogeneous term depends on the fractional derivative of lower orders were investigated respectively. Based on the expression of the solutions for this type equation, sufficient conditions for the existence of positive solutions for this type equation were obtained, also for the uniqueness. Meanwhile two examples were presented to demonstrate the main results.

Key words:  fractional differential equations, Caputo derivative, positive solution

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