带有反周期边值条件的分数阶Langevin微分包含解的存在性  

Existence of solutions for fractional Langevin differential inclusions with anti-periodic boundary value conditions

作　　者：杨丹丹 YANG Dandan(School of Mathematics and Statistics,Huaiyin Normal University,Huaian,Jiangsu 223300,China)

机构地区：[1]淮阴师范学院数学与统计学院,江苏淮安223300

出　　处：《华中师范大学学报（自然科学版）》2021年第1期1-6,14,共7页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11571136,11701206)。

摘　　要：研究如下带有反周期边值条件的分数阶Langevin微分包含:{Dβ(Dα+λ)x(t)∈F(t,x(t)),0<t<1,0<α≤1,1<β≤2,x(0)+x(1)=0,Dαx(0)+Dαx(1)=0,D2α*x(0)+D2α*x(1)=0,其中,Dα是α-阶Caputo分数阶导数,F:[0,1]×X→P(X)是一个多值映射,λ是一个实数.由多值映射的不动点定理,给出了其解的存在性的充分性条件.该文将单值情形推广到多值情形.In this paper,we investigate the existence of solutions for Langevin fractional differential inclusions with anti-periodic boundary value conditions:Dβ(Dα+λ)x(t)∈F(t,x(t)),0<t<1,0<α≤1,1<β≤2,x(0)+x(1)=0,Dαx(0)+Dαx(1)=0,D2α*x(0)+D2α*x(1)=0,where Dαis the Caputo fractional derivative of orderα,F:[0,1]×X→P(X)is a multivalued map,λis a constant.By means of some standard fixed point theorems,sufficient conditions for the existence of solutions for the fractional differential inclusions are presented.Our results generalize the single known results to the multi-valued ones.

关 键 词：Langevin微分包含 分数阶 反周期边值问题 不动点定理 

分 类 号：O175.8[理学—数学]