一类半线性分数阶微分方程解的存在性

Existence of solutions to a class of semilinear fractional differential equations

摘要:

本文考虑如下一类含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: (_^c)D_t^α u(t)+ (_^c)D_t^β u(t)=f(t,u(t) ),0β>0， (_^c)D_t^β u(t)为Caputo分数阶导数. 我们利用Schauder不动点定理证明了在适当条件下解的存在性，所得结果改进了已有结论。

Abstract:

In this paper, we consider the existence of the solutions to a class of two-term fractional initial boundary value problem: (_^c)D_t^α u(t)+ (_^c)D_t^β u(t)=f(t,u(t) ),0β>0.Our discussion is based on the Schauder fixed point theorem and our result improve some recent results.