分数阶泛函微分方程边值问题的耦合上下解方法

The method of coupled upper and lower solutions for boundary value problems of fractional functional differential equations

研究一类带时滞的分数阶泛函微分方程边值问题.首先将所研究的问题转化为积分方程形式,运用非线性分析理论证明了边值问题解的存在性与唯一性定理,产生了求边值问题解的单调迭代序列,并进行了误差估计.其次运用广义单调迭代技术和耦合上下解方法,获得了边值问题解存在唯一的充分条件,并确定了解的取值范围.最后给出几个具体实例,用于说明所得到的结论具有较广泛的适应性.

In this paper,a class of boundary value problems of fractional functional differential equations with time delays is studied.Firstly,the problems studied in this paper are transformed into integral equations.The existence and uniqueness theorems of solutions for boundary value problems are proved by using nonlinear analysis theory.The monotone iterative sequences for solving the solutions of boundary value problems are generated and the error estimates are given.Secondly,by using the generalized monotone iteration technique and the coupled upper and lower solutions method,the sufficient conditions for the existence and uniqueness of solutions of boundary value problems are obtained,and the range of solutions is determined.Finally,some examples are given to illustrate the wide applicability of our main results.