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浙江大学学报(理学版)  2017, Vol. 44 Issue (3): 287-291    DOI: 10.3785/j.issn.1008-9497.2017.03.007
数学与计算机科学     
一类分数阶非线性微分包含初值问题的可解性
杨小娟, 韩晓玲
西北师范大学 数学与统计学院, 甘肃 兰州, 730070
The solvability of Cauchy problem for nonlinear fractional differential inclusions
YANG Xiaojuan, HAN Xiaoling
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
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摘要: 在新的分数阶导数定义下,运用Bohnenblust-Karlin不动点定理并结合上下解方法研究了一类分数阶非线性微分包含初值问题的可解性.其中,FJ×R→2R是一个L1-Carathéodary函数,xαt)表示xt上的α阶导数,α∈(0,1].最后,分别给出了当集值映射F关于第二变量x次线性和至多线性增长时解的存在结果.
关键词: 微分包含分数阶导数可解性Bohnenblust-Karlin不动点定理    
Abstract: In this paper, using Bohnenblust-Karlin's fixed point theorem and combining the upper and lower solution method, we mainly study the solvability of Cauchy problem for nonlinear fractional differential inclusions where F:J×R→2R is L1-Carathéodary function, x(α)(t) denotes the conformable fractional derivative of x at t of order α, α∈(0,1]. By applying this theorem, we arrive at two existence results when the multi-valued nonlinearity F has sub-linear or linear growth about the second variable.
Key words: differential inclusions    fractionl derivatives    existence of solutions    Bohnenblust-Karlin's fixed point theorem
收稿日期: 2016-05-25 出版日期: 2017-03-01
CLC:  O175.8  
基金资助: 国家自然科学基金资助项目(11561063).
通讯作者: 韩晓玲,ORCID:http://orcid.org/0000-0002-0670-9657,E-mail:hanxiaoling9@163.com.     E-mail: hanxiaoling9@163.com
作者简介: 杨小娟(1992-),ORCID:http://orcid.org/0000-0002-7738-9021,女,硕士研究生,主要从事常微分方程边值问题研究,E-mail:18394172453@163.com.
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杨小娟, 韩晓玲. 一类分数阶非线性微分包含初值问题的可解性[J]. 浙江大学学报(理学版), 2017, 44(3): 287-291.

YANG Xiaojuan, HAN Xiaoling. The solvability of Cauchy problem for nonlinear fractional differential inclusions. Journal of Zhejiang University (Science Edition), 2017, 44(3): 287-291.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.03.007        https://www.zjujournals.com/sci/CN/Y2017/V44/I3/287

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