分数阶微分方程边值问题解的存在性

摘要

The existing of solutions for the following boundary value problem of fractional differential equations is studied.{ cDau(t) +λcDa-1u(t) +f(t, u(t)) = 0, 0 ＜ t ＜ 1, u(0) = 0, u(1) = 0,where l＜a≤2, 0≤λ＜1/8 cDa is Caputo fractional derivative, and f: [0, 1] × R→R is continuous.Under several types of sufficient conditions, the existence of solutions to the above problem is proved by a fixed-point theorems.%研究如下的分数阶微分方程边值问题解的存在性:{cDαu(t)+λcDα-1u(t)+f(t,u(t))=0,0＜t＜1,u(0)=0,u(1)=0,}其中:1＜a≤2,0≤λ＜1/8,cDα是Caputo分数阶导数,f:[0,1]×R→R是连续函数.在几组不同的充分条件下,分别运用不动点定理证明了这类边值问题解的存在性.