一类分数阶微分方程边值问题正解的存在性  

Existence of positive solutions for a class of boundary value problems of fractional differential equations

作　　者：冯立杰 FENG Li-jie(School of Mathematics,Tianjin University,Tianjin 300350,China)

机构地区：[1]天津大学数学学院,天津300350

出　　处：《东北师大学报（自然科学版）》2018年第4期32-39,共8页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61170019)

摘　　要：研究了一类带有积分边值条件的分数阶微分方程边值问题.得到了对应的格林函数,并将边值问题转化为积分算子方程.利用格林函数的性质和一些不动点定理得到该边值问题存在正解的充分性条件.最后,举例说明了结果的有效性.A class of boundary value problems of fractional differential equations with integral boundary value conditions were researched.The corresponding Green function was obtained and the boundary value problem was translated to integral operator equation.Existence of positive solutions was obtained by applying the properties of Green function and some fixed point theorems.At last,two examples were given to illustrate the advantages of the results.

关 键 词：分数阶微分方程 边值问题 正解 不动点定理 

分 类 号：O175.8[理学—数学]