一类半线性分数阶微分方程解的存在性（英文）

Existence of solutions to a class of semilinear fractional differential equations

本文考虑如下含有两项分数阶导数的半线性分数阶微分方程解的存在性问题:{~cD_t~αu(t)+λ~cD_t~βu(t)=f(t,u(t)),0<t≤h,u(0)=x_0,u′(0)=y_0,其中1<α≤2,α>β>0,~cD_t~α为Caputo分数阶导数.利用Schauder不动点定理,作者证明了在适当条件下解存在.所得结果改进了已有结论.

In this paper, based on the Schauder fixed point theorem, we consider existence of the solutions for a class of two-term fractional initial boundary value problem： {cDt^α u（t）＋λ^cDt^β u（t）=f（t,u（t） ）,0〈t≤h, u（0）=x0,u′（0）=y0, where α∈ （1,2], α〉β〉0, and the fractional derivative is in the sense of Caputo. Our results improve some recent results.