一类Riemann Liouville型分数阶微分方程积分边值问题的正解

Positive Solutions for Integral Boundary Value Problems of a Class of Riemann-Liouville-type Fractional Differential Equations

运用不动点方法研究具有Riemann-Stieltjes积分边界条件的Riemann-Liouville型分数阶微分方程的边值问题.将该方程转化成等价的积分方程,在合适的工作空间构造对应的算子方程,再借助Krasnosel’skii-Zabreiko不动点定理求解其不动点,进而获得原方程正解的存在性.

Based on the fixed point theory,this paper aims to study the boundary value problem for a Riemann-Liouville-type fractional differential equation with Riemann-Stieltjes integral boundary value conditions.Firstly,its equivalent integral equation is transformed,and the corresponding operator equation is constructed in the function space.Then,fixed points of the operator equation are obtained by using the Krasnosel’skii-Zabreiko fixed point theorem,and so the existence of positive solutions is shown for the considered problem.