具逐项分数阶导数的积分边值问题正解的存在性  

Existence of Positive Solutions for the Integral Boundary Value Problem of Sequential Fractional Differential Equations

作　　者：李燕[1] 刘锡平[1] 李晓晨[1] 张莎[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2016年第6期511-516,共6页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11171220);沪江基金资助项目(B14005)

摘　　要：研究了一类具有逐项分数阶导数的微分方程积分边值问题正解的存在性和多解性.利用锥上不动点定理和Leggett-Williams不动点定理,分别得到了该积分边值问题至少存在1个正解和3个正解的结论.最后给出2个例子来证明结论有效.The existence and multiplicity of positive solutions were investigated for a class of integral boundary value problems of fractional differential equations with sequential fractional derivatives.The existence of at least one positive solution and three positive solutions for integral boundary value peroblems was obtained respectively,by using the fixed point theorem on cone and the Leggett-Williams fixed point theorem.Two examples were given to illustrate the results.

关 键 词：分数阶微分方程 逐项分数阶导数 积分边值问题 锥上不动点定理 正解 

分 类 号：O175.8[理学—数学]