一类非线性分数微分方程正解的存在唯一性

Existence and Uniqueness of Positive Solution for a Class of Nonlinear Fractional Differential Equations

通过构造上、下控制函数,结合上、下解方法及不动点理论,研究了一类非线性项不具任何单调性的分数微分方程,获得了其正解存在性及唯一性的充分条件,推广了已有的一些结果.

In this paper,the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control function of the nonlinear terms without any monotone requirement. Our main method used in the work is the method of upper and lower solutions and Schauder fixed point theorem. Some known results are extended.