带有奇异非线性项的分数微分方程周期解的存在性与唯一性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (6): 1059-1070.

带有奇异非线性项的分数微分方程周期解的存在性与唯一性

冯育强¹, 王蔚敏², 李寿贵²

1 武汉科技大学理学院武汉 430065;
2 冶金工业过程系统科学湖北省重点实验室武汉 430081

收稿日期:2014-10-14 修回日期:2015-03-03 出版日期:2015-12-25 发布日期:2015-12-25
作者简介:冯育强,yqfeng6@126.com
基金资助:
国家自然科学基金(61473338)、教育部高等学校博士点基金(20134219120003)和湖北省自然科学基金重点项目(2013CFA131)资助

Existence and Uniqueness Results for the Periodic Boundary Value Problems of Fractional Differential Equations with Singular Nonlinearities

Feng Yuqiang¹, Wang Weimin², Li Shougui²

1 School of Science, Wuhan University of Science and Technology, Wuhan 430065;
2 Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081

Received:2014-10-14 Revised:2015-03-03 Online:2015-12-25 Published:2015-12-25

摘要/Abstract

摘要：

该文目的在于给出如下分数阶微分方程解的存在唯一性结论
D^αx(t)=f(t,x(t)),t∈J:=(0,1], 0<α<1,
t^1-αx(t)=x(1),(PBVP)
其中f在t=0可以是奇异的.主要的工具是上下解方法、最大值原理和单调迭代技术.最后举例说明所获结论的应用.

关键词: 分数微分方程, 周期边值问题, 存在性, 唯一性, 奇异性

Abstract:

The purpose of this paper is to give some sufficient conditions for the existence and uniqueness of solutions to the fractional differential equation as follows
D^αx(t)=f(t,x(t)),t∈J:=(0,1], 0<α<1,
t^1-αx(t)=x(1),
where D^α denotes the Riemann-Liouville fractional derivative, f may be singular at t=0. Lower and upper solutions method, maximum principle together with iterative technique are employed. An example is presented to illustrate the application of results obtained.

Key words: Fractional differential equation, Periodic boundary value problem, Existence, Uniqueness, Singularity

中图分类号:

O175.08

冯育强, 王蔚敏, 李寿贵. 带有奇异非线性项的分数微分方程周期解的存在性与唯一性[J]. 数学物理学报, 2015, 35(6): 1059-1070.

Feng Yuqiang, Wang Weimin, Li Shougui. Existence and Uniqueness Results for the Periodic Boundary Value Problems of Fractional Differential Equations with Singular Nonlinearities[J]. Acta mathematica scientia,Series A, 2015, 35(6): 1059-1070.

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