带有非局部积分边值的Hadamard型分数阶微分包含解的终结点型存在性定理

doi:10.6040/j.issn.1671-9352.0.2017.222

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (2): 46-51.doi: 10.6040/j.issn.1671-9352.0.2017.222

带有非局部积分边值的Hadamard型分数阶微分包含解的终结点型存在性定理

杨丹丹

淮阴师范学院数学科学学院, 江苏淮安 223300

收稿日期:2017-05-10 出版日期:2018-02-20 发布日期:2018-01-31
作者简介:杨丹丹(1982— ), 女,博士,副教授, 研究方向为非线性泛涵分析及其应用. E-mail:ydd423@sohu.com
基金资助:
国家自然科学基金资助项目(11426141);江苏省自然科学基金资助项目(BK20170067)

Endpoint theorem on existence of solutions for Hadamard-type fractional differential inclusions with nonlocal integral boundary value conditions

YANG Dan-dan

School of Mathematical Science, Huaiyin Normal University, Huaian 223300, Jiangsu, China

Received:2017-05-10 Online:2018-02-20 Published:2018-01-31

摘要/Abstract

摘要： 利用多值映射的不动点定理, 给出了以下带有非局部积分边值Hadamard型分数阶微分包含解的终结点型存在性定理:{D^αx(t)∈F(t,x(t)), 1e, 1<α≤2, x(1)=x(0), A/(Γ(γ))∫^η₁(logη/s)^γ-1(x(s))/sds+Bx(e)=c, γ>0, 1<η<e, 其中D^α表示Hadamard型分数阶导数, F:［1,e］×R→P(R)是多值映射, A,B,c是常数。所得结果将已有的单值结果推广到多值情形。

关键词: 多值映射, 边值条件, Hadamard型分数阶微分包含, 终结点定理

Abstract: Based on fixed-point theorem for multi-value maps, the endpoint theorem on the existence of solutions for the following Hadamard fractional order differential inclusions with nonlocal integral boundary value problems is given:{D^αx(t)∈F(t,x(t)), 1e, 1<α≤2, x(1)=x(0), A/(Γ(γ))∫^η₁(logη/s)^γ-1(x(s))/sds+Bx(e)=c, γ>0, 1<η<e, where D^α is Hadamard type fractional derivative, F:［1,e］×R→P(R)is a multi-valued map, A,B,c are constants. The aim of this paper is to extend known single value result to multi-valued framework.

Key words: Hadamard-type fractional differential inclusions, endpoint theorem, multi-valued maps, boundary value conditions

中图分类号:

O175.14

杨丹丹. 带有非局部积分边值的Hadamard型分数阶微分包含解的终结点型存在性定理[J]. 山东大学学报（理学版）, 2018, 53(2): 46-51.

YANG Dan-dan. Endpoint theorem on existence of solutions for Hadamard-type fractional differential inclusions with nonlocal integral boundary value conditions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 46-51.

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带有非局部积分边值的Hadamard型分数阶微分包含解的终结点型存在性定理

Endpoint theorem on existence of solutions for Hadamard-type fractional differential inclusions with nonlocal integral boundary value conditions

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