非线性分数阶泛函微分方程组边值问题的可解性

Solvability for Boundary Value Problems of Nonlinear Fractional Functional Differential Systems

本文研究了一类非线性分数阶泛函微分方程组边值问题正解的存在性。首先,将所研究的问题转化为积分方程形式,通过做变换得到等价积分方程。然后建立比较定理,运用上下解方法证明了边值问题正解的存在性。最后给出一个例子说明结论的适用性。

In this paper, the existence of positive solutions for a class of boundary value problems of nonlinear fractional functional differential system with time delays is studied. Firstly, the problems studied in this paper are transformed into integral equations, and the equivalent integral equation is obtained by transformation. Secondly, a comparison theorem is established and the existence of positive solutions of boundary value problem is proved by using upper and lower solution method. Finally, an example is given to illustrate the applicability of the conclusion.