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

作　　者：杜听说 李成福[1] DU Tingshuo;LI Chengfu(Faculty of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《应用数学》2020年第4期964-971,共8页Mathematica Applicata

基　　金：国家自然科学基金资助(10671182)。

摘　　要：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.

关 键 词：分数阶微分方程 Caputo-Hadamard导数 不动点定理 解的存在性 

分 类 号：O175.8[理学—数学]