一类具ψ-Caputo导数的分数阶微分方程边值问题解的存在性

Existence of Solutions to Boundary Value Problems for a Class of Fractional Differential Equations withψ-Caputo Derivatives

分数阶微分方程的研究可以解决数学、空气动力学、经济学、聚合物流变学等多个领域的复杂问题;在一类具ψ-Caputo导数的分数阶微分方程边值问题中,其中边值条件包含多点和积分,首先由ψ-Caputo导数的定义和性质获得解的等价积分方程形式,接着该边值问题解的唯一性与存在性分别由Banach压缩映像原理和Schauder不动点定理获得,最后,通过一个实例说明了结果的应用性。

The study of fractional differential equation can settle numerous tanglesome matters in mathematics,aerodynamics,economics,polymer rheology and other fields.In a class of boundary value problems for fractional differential equations withψ-Caputo derivatives,the boundary value conditions contain multiple points and integrals,the form of the solution of the isovalent integral equation is first gained from the definition and properties ofψ-Caputo derivative,afterwards,the uniqueness and existence of the solution of the boundary value problem are gained by the Banach contraction mapping principle and Schauder fixed point theorem respectively.In the end,the application of the result is illustrated by an example.