分数阶时滞微分方程积分边值问题解的存在性

J4 ›› 2013, Vol. 48 ›› Issue (12): 24-29.

分数阶时滞微分方程积分边值问题解的存在性

李凡凡,刘锡平*,智二涛

上海理工大学理学院, 上海 200093

收稿日期:2013-07-11 出版日期:2013-12-20 发布日期:2014-01-09
通讯作者: 刘锡平(1962-),男,教授,研究方向为常微分方程理论及应用. Email: xipingliu@163.com
作者简介:李凡凡(1986-),女,硕士研究生,研究方向为常微分方程理论及应用. Email: lifanfan1208@126.com
基金资助:
国家自然科学基金资助项目(11171220)

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

LI Fan-fan, LIU Xi-ping*, ZHI Er-tao

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2013-07-11 Online:2013-12-20 Published:2014-01-09

摘要/Abstract

摘要：

研究一类具有Riemann-Liouville型分数导数的分数阶时滞微分方程积分边界问题。根据方程及边界条件的特点, 给出了上下解的定义, 并证明了比较定理。利用上下解方法, 结合单调迭代技术以及度理论, 得到了边值问题解的存在性定理、惟一性定理以及多解性定理多个结论。

关键词: 时滞;分数阶微分方程;边值问题;单调迭代技术;上下解;LeraySchauder度

Abstract:

It is studied that the boundary value problem for a class of fractional delay differential equations with Riemann-Liouville fractional derivative. According to the boundary conditions, the definition of upper and lower solutions are given, and the comparison theorem is proved. By using the method of upper and lower solutions, monotone iterative technique and topological degree theory, existence and uniqueness theorems and multiple theorems are obtained.

Key words: delay; fractional differential equation; boundary value problem; monotone iterative technique; upper and lower solutions; Leray-Schauder degree

中图分类号:

O175.8

李凡凡,刘锡平*,智二涛. 分数阶时滞微分方程积分边值问题解的存在性[J]. J4, 2013, 48(12): 24-29.

LI Fan-fan, LIU Xi-ping*, ZHI Er-tao. Existence of a solution for the boundary value problem of
fractional differential equation with delay[J]. J4, 2013, 48(12): 24-29.

参考文献

相关文章 8

[1]	俎冠兴. 边值问题的多重正解[J]. J4, 2009, 44(12): 71-76.
[2]	姚庆六. 一类奇异次线性Sturm Liouville 边值问题[J]. J4, 2009, 44(10): 36-38.
[3]	许万银. 一类拟线性Neumann问题的多重解[J]. J4, 2009, 44(10): 39-42.
[4]	代丽美. 正指数Emden-Fowler方程脉冲奇异边值问题的PC¹(［0,1］,R₊)正解[J]. J4, 2008, 43(12): 10-14.
[5]	续晓欣梁月亮桑彦彬. 三阶两点边值问题单调递减正解的存在惟一性[J]. J4, 2008, 43(12): 84-87.
[6]	唐秋云,王明高,刘衍胜 . 高阶p-Laplacian算子方程组边值问题多个正解的存在性[J]. J4, 2008, 43(5): 50-53 .
[7]	徐玲 . 上下解方法与三点边值共振问题的可解性[J]. J4, 2008, 43(5): 66-70 .
[8]	秦小娜,贾梅*,刘帅. 具Caputo导数分数阶微分方程边值问题正解的存在性[J]. J4, 2013, 48(10): 62-67.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed