非线性分数阶微分方程边值问题正解的存在性与唯一性

Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem

研究非线性分数阶微分方程边值问题。利用带有扰动的混合单调算子不动点定理,证明其正解的存在唯一性,同时构造一迭代序列去逼近该正解。举例应用了所得的主要结果。

This paper is concerned with the existence and uniqueness of positive solutions for boundary value problem of nonlinear fractional differential equations. By using new fixed point theorem for mixed monotone operator with perturbation, the existence and u- niqueness of its positive solution is proved,and an iterative scheme is constructed to approximate it. Finally, the example is given to il- lustrate the application of the main result.