[1]郭成,丁卯松,韩筱爽*.带有分数阶边值条件的分数阶差分方程的正解[J].延边大学学报(自然科学版),2015,41(01):25-29.
　GUO Cheng,DING Maosong,HAN Xiaoshuang*.Existence of positive solution for a fractional difference equations with fractional boundary value condition[J].Journal of Yanbian University,2015,41(01):25-29.
点击复制

带有分数阶边值条件的分数阶差分方程的正解

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第41卷 期数: 2015年01期 页码: 25-29 栏目: 基础科学研究 出版日期: 2015-03-20
Title:
Existence of positive solution for a fractional difference equations with fractional boundary value condition
作者:
郭成; 丁卯松; 韩筱爽*
延边大学 科学技术学院, 吉林 延吉 133002
Author(s):
GUO Cheng;  DING Maosong;  HAN Xiaoshuang*
Institute of Science and Technology, Yanbian University, Yanji 133002, China
关键词:
分数阶边值条件;  Green函数;  正解
Keywords:
fractional order boundary value condition;  Green’s function;  positive solution
分类号:
O175.6
文献标志码:
A
摘要:
研究了一类带有分数阶边值条件的分数阶差分方程正解的存在性问题.首先利用分数阶差分方程理论和边值条件给出了解的结构,其次分析了Green函数的一些性质,最后利用锥上的不动点定理证明了该问题正解的存在性.
Abstract:
We study the existence of positive solutions of the boundary value problem for a fractional difference equation with fractional boundary value condition. Firstly, according to the theory of fractional difference equation and its boundary conditions, we got the structure of solutions, then analyze some properties of the Green’s function, at last, the existence of the positive solutions of the problem is proved by using the fixed point theorem in cones.

参考文献/References:

[1] Atici F M, Eloe P W. Two-point boundary value problems for finite fractional difference equations[J]. J Difference Equ Appl, 2011,17(4):445-456.
[2] Goodrich C S. Solutions to a discrete right-focal boundary value problem[J]. Int J Difference Equ, 2010,5:195-216.
[3] Goodrich C S. Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions[J]. J Comput Math Appl, 2011,61(21):191-202.
[4] Goodrich C S. On a fractional boundary value problem with fractional boundary conditions[J]. J Applied Mathematics Letters, 2012,25:1101-1105.
[5] Miller K S, Ross B. Fractional difference calculus, procedings of the internations symposium on Univalent functions[J]. Fractional Calculus and their Applications Nihon University, 1988,1(4):139-152.
[6] Atici F M, Eloe P W. A transform method in discrete fractional calculus[J]. Int J Difference Equ, 2007,2(2):165-176.
[7] Atici F M, Eloe P W. Initial value problems in discrete fractional calculus[J].Proc Amer Math Soc, 2009,137:981-989.
[8] 时宝,张德存,盖久明.微分方程理论及其应用[M].北京:国防工业出版社,2005:13.
[9] 程金发.分数阶差分方程理论[M].厦门:厦门大学出版社,2010.

相似文献/References:

[1]杨慧,王文霞.一类高次分数阶微分方程正解的存在唯一性[J].延边大学学报(自然科学版),2013,39(03):167.
　YANG Hui,WANG Wenxia.Existence and uniqueness of the positive solution of a class of high-order fractional differential equation[J].Journal of Yanbian University,2013,39(01):167.
[2]祝相宇,孙明哲.一类分数阶差分方程正解的存在性[J].延边大学学报(自然科学版),2014,40(01):25.
　ZHU Xiangyu,SUN Mingzhe.Existence of positive solution for a class of fractional difference equations[J].Journal of Yanbian University,2014,40(01):25.

备注/Memo

收稿日期: 2014-09-21 基金项目: 延边大学自然科学基金资助项目(延大科合字2013第11号)*通信作者: 韩筱爽(1980—),女,讲师,研究方向为可靠性与微分方程理论.

更新日期/Last Update: 2015-03-20