具有微分算子的分数阶微分方程边值问题解的存在性与唯一性

Existence and Uniqueness of Solutions for Boundary Value Problems of Fractional Differential Equations with Differential Operator

研究一类具有分数阶线性微分算子的Riemann-Liouville型分数阶非线性微分方程两点边值问题解的存在性和唯一性.通过求出相应边值问题的Green函数并证明其性质,建立积分算子方程,应用压缩映射原理证明了这类边值问题解的存在性与唯一性定理.运用Krasnoselskii’s不动点理论建立并证明了该边值问题解的存在性与唯一性定理.最后给出了两个应用实例,用以说明本文所得结论的有效性.

The existence and uniqueness of solutions for a class of two points boundary value problems of Riemann-LiouviUe nonlinear fractional differential equation with linear fractional differential operator were considered. Through finding the Green function of the boundary value problem and determining its properties,an integral operator equation was established and some sufficient conditions for the existence and uniqueness of solutions were derived by applying the contraction principle and the fixed point theorem. Some examples were given to illustrate the results.