Caputo-Hadamard型分数阶微分方程边值问题解的存在唯一性(英文)

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR CAPUTO-HADAMARD TYPE FRACTIONAL DIFFERENTIAL EQUATIONS

本文研究了一类Caputo-Hadamard型分数阶微分方程边值问题的解.利用Banach不动点定理和上下解方法,获得了解的存在性和唯一性,推广了常微分方程边值问题的一些结果.作为应用,给出了两个例子来说明我们的主要结果.

In this paper, we study a class of Caputo-Hadamard fractional differential equations with boundary value problems. By using Banach fixed point theorem and the method of upper and lower solutions method, the existence and uniqueness results of the solutions are obtained, which generalizes some results about ordinary differential equations with boundary value problems. As an application, two examples are given to illustrate our main results.