一类具有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在唯一性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1162-1172.

一类具有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在唯一性

贠永震,苏有慧*(),胡卫敏

¹ 徐州工程学院数学与物理科学学院江苏徐州 221000
² 伊犁师范学院数学与统计学院新疆伊宁 835000

收稿日期:2016-11-15 出版日期:2018-12-26 发布日期:2018-12-27
通讯作者: 苏有慧 E-mail:suyh02@163.com
基金资助:
国家自然科学基金(11361047);国家自然科学基金(11501560);江苏省自然科学基金(BK20151160);江苏省六大人才高峰项目(2013-JY-003);江苏省333高层次人才项目(BRA2016275)

Existence and Uniqueness of Solutions to a Class of Anti-Periodic Boundary Value Problem of Fractional Differential Equations with p-Laplacian Operator

Yongzhen Yun,Youhui Su*(),Weimin Hu

¹ School of Mathematics and Physics, Xuzhou Institute of Technology, Jiangsu Xuzhou 221000
² School of Mathematics and Statistic, Yili Normal University, Xinjiang Yining 835000

Received:2016-11-15 Online:2018-12-26 Published:2018-12-27
Contact: Youhui Su E-mail:suyh02@163.com
Supported by:
the NSFC(11361047);the NSFC(11501560);the Natural Science Foundation of Jiangsu Province(BK20151160);the Six Talent Peaks Project of Jiangsu Province(2013-JY-003);the 333 High-Level Talents Training Program of Jiangsu Province(BRA2016275)

摘要/Abstract

摘要：

该文研究了一类具有p-Laplacian算子的非线性Caputo分数阶微分方程反周期边值问题解的存在唯一性.首先，利用分数阶微分方程和反周期边值条件给出了该边值问题的Green函数，然后利用p-Laplacian算子的性质和Banach压缩映射原理得到该边值问题解的存在唯一性结论，最后给出两个例子验证结论的合理性.值得一提的是此文研究的微分方程的反周期边值条件是带有Caputo分数阶微分.

关键词: Caputo分数阶微分, 反周期边值问题, 解的存在唯一性, p-Laplacian算子, Banach压缩映射原理

Abstract:

In this paper, we investigate the existence and uniqueness of solutions to a class of anti-periodic boundary value problem of nonlinear Caputo fractional differential equations with p-Laplacian operator. First, the Green function of the fractional boundary value problem is given. By using the properties of p-Laplacian operator and the Banach contraction mapping principle, some new results on the existence and uniqueness of solutions to the fractional boundary value problem are obtained. As an application, two examples are given to illustrate our main results. In particular, the boundary value conditions of fractional differential equation which is studied in this paper contains the Caputo fractional differentiation.

Key words: Caputo fractional differentiation, Anti-periodic boundary value problem, Existence and uniqueness of solutions, p-Laplacian operator, Banach contraction mapping principle

中图分类号:

O175.8

贠永震,苏有慧,胡卫敏. 一类具有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在唯一性[J]. 数学物理学报, 2018, 38(6): 1162-1172.

Yongzhen Yun,Youhui Su,Weimin Hu. Existence and Uniqueness of Solutions to a Class of Anti-Periodic Boundary Value Problem of Fractional Differential Equations with p-Laplacian Operator[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1162-1172.

参考文献 13

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