一类Hadamard分数阶微分方程边值问题解的存在唯一性

Existence and uniqueness of solution for boundary value problems of a class of Hadamard fractional differential equations

作者：张海燕(宿州学院数学与统计学院)；李耀红(宿州学院数学与统计学院)

Author：ZHANG Hai-Yan(School of Mathematics and Statistics, Suzhou University)；LI Yao-Hong(School of Mathematics and Statistics, Suzhou University)

收稿日期：2017-09-01 年卷（期）页码：2018,55(4):683-687

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：Hadamard分数阶导数; 分数阶微分方程; 边值条件; 存在唯一性

Key words：Hadamard fractional derivative; Fractional differential equation; Boundary value problem; Existence and uniqueness

基金项目：安徽省高等学校自然科学基金重点项目基金（KJ2017A442，KJ2017A702,KJ2018A0452）；安徽省高校优秀青年人才支持计划重点项目基金（gxyqZD2016339）；宿州学院优秀青年学术骨干项目基金（2016XJGG13）

中文摘要

利用Leray-Schauder选择原理及Banach压缩映射原理,本文在一定的非线性增长和压缩条件下研究了一类具有Hadamard积分边值条件的Hadamard分数阶微分方程边值问题, 获得了该问题解的存在唯一性的充分条件,并给出了两个具体例子.

英文摘要

By using the Leray-Schauder’s alternative principle and Banach’s contraction principle and combined with some nonlinear growth and contraction conditions, a class of Hadamard fractional differential equations with Hadamard integral boundary conditions are investigated. Existence and uniqueness of solution for the relevant boundary value problems are established. Two examples are given to illustrate the application of the results．

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论文摘要

一类Hadamard分数阶微分方程边值问题解的存在唯一性

Existence and uniqueness of solution for boundary value problems of a class of Hadamard fractional differential equations