一类分数阶微分方程边值问题解的存在性和唯一性

Existence and Uniqueness of Solutions for the Boundary Value Problem about Fractional Differential Equation

文章主要考虑如下分数阶微分方程的边值问题Dα0+u(t)+f(t,u(t))=0,u(0)=u(1)=0.这里t∈[0,1],f:[0,1]×R→R,f为连续函数,1<α≤2.我们利用Banach压缩映射定理和Brou-wer不动点定理得到此边值问题解的存在性定理.

We investigate the existence of solutions for the boundary value problem on the following fractional differential equationD0＋U（t）＋f（t,w（t））=0,u（0）=u（1）=0where f. [-0,1] ）〈R---R is continuous, By means of the contraction mapping theorem and the Brouwer fixed point theorem,the existence and uniqueness of solution are obtained.