[1]杨军,刘东利.高阶分数阶微分方程边值问题解的存在性[J].华侨大学学报(自然科学版),2013,34(6):716-720.[doi:10.11830/ISSN.1000-5013.2013.06.0716]
　YANG Jun,LIU Dong-li.Existence of Solutions for Boundary Value Problem of Fractional High-Order Differential Equations[J].Journal of Huaqiao University(Natural Science),2013,34(6):716-720.[doi:10.11830/ISSN.1000-5013.2013.06.0716]
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高阶分数阶微分方程边值问题解的存在性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第34卷
期数:
2013年第6期
页码:
716-720
栏目:
出版日期:
2013-11-20

文章信息/Info

Title:
Existence of Solutions for Boundary Value Problem of Fractional High-Order Differential Equations
文章编号:
1000-5013(2013)06-0716-05
作者:
杨军1; 2;  刘东利1
1. 燕山大学 理学院, 河北 秦皇岛 066004; 2. 河北省数学研究所, 河北 石家庄 050000
Author(s):
YANG Jun1; 2;  LIU Dong-li1
1. College of Science, Yanshan University, Qinhuangdao 066004, China; (2. Mathematics Research Center in Hebei Province, Shijiazhuang 050000, China
关键词:
分数阶;  微分方程;  高阶;  边值问题;  不动点定理
Keywords:
fractional order;  differential equations;  high-order;  boundary value problem;  fixed point theorems
分类号:
O175.8
DOI:
10.11830/ISSN.1000-5013.2013.06.0716
文献标志码:
A
摘要:
研究一类非线性分数阶高阶微分方程边值问题解的存在性.通过定义一个特殊的压缩映射,利用Banach不动点定理和Leray-Shauder非线性抉择定理,得到所研究方程存在唯一解和至少存在一个解的充分条件,并分别给出一个例子来验证主要结果.
Abstract:
The paper mainly studies the existence of solutions for a class of nonlinear fractional higher order differential equation with boundary value problem. By defining a special compression mapping, and using Banach fixed point theorem and Leray-Shauder nonlinear decision theorem, we obtain the sufficient conditions of unique solution and at least one solution for the considered equations. Finally, examples are given to verify the main results respectively.

参考文献/References:

[1] OLDHAM K B,SPANIER J.The fractional calculus[M].New York:Academic Press,1974:181-195.
[2] HILFER R.Applications of fractional calculus in physics[M].Singapore:World Scientific,2000:50-377.
[3] LAKSHMIKANTHAM V,LEELA S,Vasundhara Devi J.Theory of fractional dynamic systems[M].Cambridge:Cambridge Academic Publishers,2009:5-60.
[4] MA Jun-chi,YANG Jun.Existence of solutions for multi-point boundary value problem of fractional q-differential equation[J].Electronic Journal of Qualitative Theory of Differential Equations,2011(92):1-10.
[5] MA Jun-chi,YANG Jun.Existence and uniqueness of solutions for multi-point fractional boundary value problems for nonlinear fractional integro-differential equations[J].Mathematica Applicata,2011,24(3):575-580.
[6] 杨军,马俊驰,赵硕,等.分数阶微分方程多点分数阶边值问题[J].数学实践与认识,2011,41(11):188-194.
[7] MA J C,YANG J.Positive solutions of the multiple point boundary value problems for nonlinear fractional differential equations[C]//The 2nd International Conference on Multimedia Technology.Hangzhou:IEEE Computer Society,2011:2293-2296.
[8] WANG Xu-huan.Existence of solutions for nonlinear impulsive high order fractional differential equations[J].Electronic Journal of Qualitative Theory of Differential Equations,2011(80):1-12.
[9] BAI Zhang-bing,LYU Hai-shen.Positive solutions for boundary value problem of nonlinear fractional differential equation[J].J Math Anal Appl,2005,311(2):495-505.
[10] EL-SHAHED M A. Positive solutions for boundary value problem of nonlinear fractional differential equations[J].Abstract and Applied analysis,2007,2007:1-8.
[11] LIANG S H,ZHANG J H.Positive solutions for boundary value problem of nonlinear fractional differential equation[J].Nonlinear Analysis,2009,71(11):5545-5550.
[12] LIU X P,JIA M.Multiple solutions for fractional differential equations with nonlinear boundary conditions[J].Computers and Mathematics with Applications,2010,59(8):2880-2886.
[13] 窦丽霞,刘锡平,金京福,等.分数阶积分微分方程多点边值问题解的存在性和唯一性[J].上海理工大学学报,2011,33(5):51-55.

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备注/Memo

备注/Memo:
收稿日期: 2013-04-26
通信作者: 杨军(1964-),女,教授,主要从事分数阶微分方程的研究.E-mail:jyang@ysu.edu.cn.
基金项目: 国家自然科学基金资助项目(60604004); 河北省应用基础研究计划重点基础研究项目(13961806D); 河北省秦皇岛市科技支撑计划项目(201001A037, 201101A168)
更新日期/Last Update: 2013-11-20