分数阶导数的非线性微分方程边值问题

The Boundary Value Problem of Nonlinear Differential Equation of Fractional Derivative is Obtained by Continuous Function

利用连续函数研究分数阶导数的非线性微分方程边值问题.通过确界定理和单调有界定理,结合构造方法对连续函数进行构造.在给定分数阶导数的条件下,引入扰动方法,利用Green函数定义非线性分数阶导数的微分方程积分算子,运用Banach压缩映像理论,证明了在连续函数空间内分数阶导数的非线性微分方程边值存在唯一解.

The nonlinear differential equations of fractional derivative boundary value problem is studied by using continuous functions.A continuous function is constructed by supremum theorem and monotone bounded theorem combined with the construction method.The fractional derivative is given under the condition of introducing perturbation method,differential equation of nonlinear fractional integral operators is defined by the derivative of Green function.Banach compressed image theory has proved in continuous function space of nonlinear differential equations of fractional derivative boundary value has a unique solution.