带有积分边值条件的两项分数阶微分方程正解的存在性  

The Existence of Positive Solutions for Integral Boundary Value Problem of Two-Term Fractional Differential Equations

作　　者：孙园园 周宗福[1] SUN Yuanyuan;ZHOU Zongfu(School of Mathematical Science,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《应用数学》2020年第2期318-326,共9页Mathematica Applicata

基　　金：国家自然科学基金(11371027);安徽省自然科学基金(1608085MA12)。

摘　　要：主要研究一类带有积分边值条件的两项分数阶微分方程在不同条件下正解的存在性及存在唯一性.利用上下解理论与Schauder不动点定理相结合的方法,得到正解的存在性.利用Banach压缩映像原理,推出正解的存在唯一性.并给出两个例子来说明结果的应用性.In this paper,we mainly study the existence and the existence and uniqueness of positive solutions for a class of two-term fractional differential equations with integral boundary value problem under different conditions.By the Schauder fixed point theorem combined with the method of upper and lower solutions,the existence of positive solution is found out.We also obtain the existence and uniqueness of the positive solution by using Banach contraction mapping principle.And two examples are given to show the applicability of the results in this paper.

关 键 词：分数阶微分方程 积分边值问题 Riemann-Liouville分数阶导数 不动点定理 

分 类 号：O175.8[理学—数学]