奇异分数阶微分方程边值问题正解的唯一性

摘要

By the means of the Green’s function, the boundary value problem of fractional dif-ferential equation can be reduced to the equivalent integral equation. Recently, this method is applied successfully to discuss the existence of the solution to boundary value problem of nonlinear fractional differential equation. This article investigates the uniqueness of positive solutions for a singular nonlinear boundary value problem of differential equations of fractional order. Our analysis relies on the fixed point theorem in partially ordered sets and the reduction of the considered problem to the equivalent of integral equations.%应用Green函数将分数阶微分方程边值问题可转化为等价的积分方程。近来此方法被应用于讨论非线性分数阶微分方程边值问题解的存在性。本文讨论奇异非线性分数阶微分方程边值问题正解的唯一性。应用Green函数将其转化为等价的积分方程，利用偏序集上的不动点定理证明正解的唯一性。