分数阶时滞微分方程积分边值问题解的存在性  

Existence of a solution for the boundary value problem of fractional differential equation with delay

作　　者：李凡凡[1] 刘锡平[1] 智二涛 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《山东大学学报（理学版）》2013年第12期24-29,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11171220)

摘　　要：研究一类具有Riemann-Liouville型分数导数的分数阶时滞微分方程积分边界问题。根据方程及边界条件的特点,给出了上下解的定义,并证明了比较定理。利用上下解方法,结合单调迭代技术以及度理论,得到了边值问题解的存在性定理、惟一性定理以及多解性定理多个结论。It is studied that the boundary value problem for a class of fractional delay differential equations with Rie-mann-Liouville fractional derivative. According to the boundary conditions, the definition of upper and lower solutions are given, and the comparison theorem is proved. By using the method of upper and lower solutions, monotone iterative technique and topological degree theory, existence and uniqueness theorems and multiple theorems are obtained.

关 键 词：时滞 分数阶微分方程 边值问题 单调迭代技术 上下解 Leray—Schauder度 

分 类 号：O175.8[理学—数学]