高阶分数阶微分方程边值问题正解的存在性

Existence of Positive Solutions for Boundary Value Problem of Fractional High-order Differential Equations

研究了一类非线性分数阶高阶微分方程边值问题正解的存在性,通过对相应分数阶Green函数的研究,并利用Banach不动点定理和Guo-Krasnosel’skii不动点定理,得到方程存在唯一正解和至少存在一个正解的充分条件,最后给出一个例子来验证其中的主要结果.

The problem of the existence of positive solutions for a class of nonlinear fractional high-order differential equations with boundary value problem was studied. By studying the corresponding Green function, and using the Banach fixed point theorem and Guo-Krasnosel＇ skii fixed point theorem, some sufficient conditions were established for the existence of unique positive solution and at least one positive solutions. Further more, one example was presented to illustrate the main result.