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

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.