高阶分数阶微分方程边值问题解的存在性

Existence of Solutions for Boundary Value Problem of Fractional High-Order Differential Equations

研究一类非线性分数阶高阶微分方程边值问题解的存在性.通过定义一个特殊的压缩映射,利用Banach不动点定理和Leray-Shauder非线性抉择定理,得到所研究方程存在唯一解和至少存在一个解的充分条件,并分别给出一个例子来验证主要结果.

The paper mainly studies the existence of solutions for a class of nonlinear fractional higher order differential equation with boundary value problem. By defining a special compression mapping, and using Banach fixed point theorem and Leray-Shauder nonlinear decision theorem, we obtain the sufficient conditions of unique solution and at least one .solu- tion for the considered equations. Finally, examples are given to verify the main results respectively.