分数阶微分方程耦合系统边值问题解的存在性

The Existence of Solution to Boundary Value Problems for a Coupled System of Nonlinear Fractional Differential Equations

应用Green函数将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分数阶微分方程边值问题正解的存在性。本文讨论非线性分数阶微分方程耦合系统的两点边值问题,应用Green函数,将其转化为等价的积分方程耦合系统,并设非线性项在无穷远处有增长条件,应用Schauder不动点定理证明解而非限于正解的存在性。

By the means of the Green＇s function, the boundary value problem of differential equation can be reduced to the equivalent integral equation. Recently, this method is used successfully to discuss the existence of the positive solution to boundary value problem of nonlinear fractional differential equation. This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.