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带积分边界条件的非线性Caputo型分数阶微分方程边值问题解的存在唯一性
Existence and Uniqueness of Solutions for Boundary Value Problems of Nonlinear Caputo Fractional Differential Equation with Integral Boundary Conditions

DOI: 10.12677/PM.2021.117151, PP. 1341-1347

Keywords: 分数阶微分方程，边值问题，解，存在性，唯一性
Fractional Differential Equation, Boundary Value Problem, Solution, Existence, Uniqueness

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Abstract:

为了更好地利用分数阶微分方程的优良性质解决工程问题，探究分数阶微分方程边值问题解的性质就成为一项重要的任务。运用Schaefer不动点定理和Banach压缩映射原理，研究一类带积分边值条件的非线性Caputo型分数阶微分方程边值问题，得到了边值问题解的存在唯一性结果。
In order to make better use of the excellent properties of fractional differential equations to solve engineering problems, it is an important task to explore the properties of solutions of boundary value problems of fractional differential equations. By using Schaefer’s fixed point theorem and Banach contraction mapping principle, the boundary value problem of a class of nonlinear Caputo type fractional differential equation with integral boundary value conditions is studied. The ex-istence and uniqueness of solutions of the boundary value problem are obtained.

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