一类分数阶微分方程边值问题解的存在性

J4 ›› 2013, Vol. 48 ›› Issue (8): 45-49.

一类分数阶微分方程边值问题解的存在性

周文学1,2, 刘海忠1

1. 兰州交通大学数学系, 甘肃兰州 730070; 2. 复旦大学数学科学学院, 上海 200433

收稿日期:2012-09-04 出版日期:2013-08-20 发布日期:2013-08-21
作者简介:周文学(1976- ),男, 博士, 副教授,研究方向为非线性分析理论及其应用. Email:wxzhou2006@126.com
基金资助:
国家自然科学基金资助项目(11161027, 11262009)

Existence of solution for the boundary value problem of a class of fractional differential equation

ZHOU Wen-xue1,2, LIU Hai-zhong1

1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070， Gansu, China;
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received:2012-09-04 Online:2013-08-20 Published:2013-08-21

摘要/Abstract

摘要：

研究了一类分数阶微分方程边值问题。应用Green函数,将分数阶微分方程边值问题转化为等价的积分方程, 利用Schaefer不动点定理和LeraySchauder不动点定理得到了该边值问题存在解的充分条件, 推广和完善了已有的结果。

关键词: 边值问题; 分数阶微分方程;Caputo型分数阶导数; 不动点定理

Abstract:

A class of boundary value problem of fractional differential equation is studied. By the means of the Green′s function, the boundary value problem of fractional differential equation can be reduced to the equivalent integral equation, and some sufficient conditions on the existence of solution for the boundary value problem are obtained by using Schaefer′s fixed point theorem and Leray-Schauder fixed point theorem. Some known results are extended and improved.

Key words: boundary value problem; fractional differential equation; Caputo fractional derivative; fixed point theorem

周文学1,2, 刘海忠1. 一类分数阶微分方程边值问题解的存在性[J]. J4, 2013, 48(8): 45-49.

ZHOU Wen-xue1,2, LIU Hai-zhong1. Existence of solution for the boundary value problem of a class of fractional differential equation[J]. J4, 2013, 48(8): 45-49.

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