非线性分数阶微分方程三点边值问题解的存在性(英文)

Existence of Solution for a Three-point Boundary Value Problem of Nonlinear Fractional Differential Equation

讨论了一类非线性分数阶微分方程三点边值问题解的存在性.微分算于是Riemann-Liouville导算子并且非线性项依赖于低阶分数阶导数.通过将所考虑的问题转化为等价的Fredholm型积分方程,利用Schauder不动点定理获得该三点边值问题至少存在一个解.

In this paper, we discuss a three-point boundary value problem for a nonlinear differ- ential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least one solution for integral equation using Schauder fixed-point theorem. Our analysis relies on the reduction of the problem considered considered to the equivalent Fredholm integral equation.