摘要
很多领域的实际问题可以建立分数阶微分方程或者微分包含模型进行研究,近年来分数阶微积分受到广泛关注。2016年,文献[8]研究了一类带有多点边值条件的分数阶微分方程解的存在性。本文中,利用多值映射的不动点定理,给出了以下带有多点边值分数阶微分包含解的Filippov型存在性定理:D~αy(t)∈F(t,y(t)),t∈[0,T],T>0,y(T)=y~*+h(x),D^Py(T)=m∑i=1D^py(ηi),其中1<α≤2,0<p<1,D~α,D^p表示Caputo导数,y~*∈R,h:[0,T]×R→R是连续函数,F:[0,T]×R→P(R)是[0,T]的多值映射,0<η_i<T,i=1,2,3,...,m。所得结果将已有的单值结果[8]推广到多值情形。
In many research fields.some practical problems could be established to fractional differential equation modelsor fractional differential inclusion models for study.which have been got much attention by mathematicians in recentyears. In 2016.in paper[8] the authors investigated the existence of solutions for a class of fractional differentialequations. In this paper.based on fixed-point theorem for multi-value maps.we are concerned with the following fractionalorder differential inclusions with multi-point boundary value problems：Dα y（t） ∈ F（t.y（t））.t ∈ [0.T].T 〉 0.y（T） = y. ＋ h（y）.DP y（T） = Σmi = 1Dp y（ηi ）.where 1 〈 α ≤2.0 〈 p 〈 1.Dα .Dp denote Caputo derivatives. x. ∈ R.0 〈 ηi 〈 T.i = 1.2.3.. . . .m. h：[0.T] × R→ R is a continuous. F：[0.T] × R → P（R） in [0.T] is a multi-valued map. The Filippove theorem on the existence ofsolutions for the problem is given. The aim of this paper is to extend known single value result[8] to multi-valued framework.
作者
杨丹丹
YANG Dan-dan(School of Mathematical Science,Huaiyin Normal University,Huaian 223300,Chin)
出处
《安徽师范大学学报（自然科学版）》
CAS
2018年第2期121-128,共8页
Journal of Anhui Normal University(Natural Science)
基金
国家自然科学基金项目(11426141)
江苏省自然科学基金项目(BK20151288)
关键词
分数阶微分包含
边值条件
Filippov定理
多值映射
fractional differential inclusions.boundary value conditions.Filippov＇s Theorem.multi-valued maps
