具有Caputo-Hadamard导数的分数阶微分方程边值问题

Boundary Value Problem of Fractional Differential Equation with Caputo-Hadamard Derivative

本文研究一类具有Caputo-Hadamard导数的分数阶微分方程边值问题.利用巴拿赫不动点定理、Krasnosel’skii不动点定理、非线性二择一定理和Leray-Schauder度,得到边值问题解的存在性,并用一些例题验证了研究结果.

In this paper,we study the existence of solution for boundary value problem of fractional differential equations with the Caputo-Hadamard derivative.We obtain the existence of solution by using Banach’s fixed point theorem,Krasnosel’skii fixed point theorem,Leray-Schauder’s nonlinear alternative and Leray-Schauder degree.Some examples are presented to illustrate our main results.