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

作者：郑荟萃(四川大学数学学院)；李淼(四川大学数学学院)

Author：ZHENG Hui-Cui(College of Mathematics, Sichuan University)；LI Miao(College of Mathematics, Sichuan University)

收稿日期：2016-03-27 年卷（期）页码：2017,54(1):29-34

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：分数阶微分方程, Caputo导数, Schauder不动点定理

Key words：Fractional differential equations, Caputo fractional derivatives, Schauder fixed point theorem

基金项目：

中文摘要

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。

英文摘要

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.

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论文摘要

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