一类带有偏差量的任意分数阶非线性微分方程边值问题唯一正解的存在性

The existence and uniqueness of positive solutions for a class of boundary value problems of arbitrary fractional order differential equations with deviated arguments

该文研究了一类带有偏差量的任意分数阶非线性微分方程边值问题正解的存在唯一性,利用锥理论及混合单调算子和算子不动点定理获得了该边值问题存在唯一正解的充分条件,并给出了一个具体的例子以显示理论结果.

In this paper, the existence and uniqueness of positive solutions for a class of boundary value problems of arbitrary fractional order nonlinear differential equations with deviated arguments is studied. By using the cone theory and the fixed point theorem for the sum of mixed monotone operators, sufficient conditions for existence of the unique positive solution for the boundary value problems are obtained. An example is given to illustrate theoretical results.