一类分数阶微分方程的积分边值问题  

Integral Boundary Value Problem of a Class of Fractional Differential Equations

作　　者：高珊珊 吴睿 GAO Shan-shan;WU Rui(Department of Basic Teaching,Liaoning Institute of Science and Engineering,Jinzhou 121000,China;Department of Mathematics,Changchun University of Finance and Economics,Changchun 130122,China)

机构地区：[1]辽宁理工学院基础教学部,辽宁锦州121000 [2]长春财经学院数学教研部,吉林长春130122

出　　处：《数学的实践与认识》2021年第22期199-203,共5页Mathematics in Practice and Theory

基　　金：吉林省自然科学基金(20200201274JC)。

摘　　要：研究了一类Caputo型分数阶微分方程在积分边值条件下的解的存在性的问题.首先利用Leray-Schauder不动点定理证明了该分数阶非线性微分方程解的存在性,再利用分数阶不等式理论进一步证明了该解的唯一性.最后给出了一个应用实例.This paper is devoted to study the existence of solutions for a class of Caputo type fractional differential equations under integral boundary value conditions.First,the Leray-Schauder fixed point theorem is used to prove the existence of the solutions of the fractional nonlinear differential equations,and then use the theory of fractional inequalities further to prove the uniqueness of the solution.Finally,an application example is given.

关 键 词：Caputo型分数阶微分 分数阶微分方程 积分边值 LERAY-SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]