带有Stieltjes积分边界条件和ψ-Caputo导数的分数阶边值问题解的存在性

Existence of Solutions for Fractional Boundary Value Problems withψ-Caputo Derivative and Stieltjes Integral Boundary Conditions

考虑一类带有ψ-Caputo分数阶导数的分数阶微分方程边值问题,其边界条件含有Stieltjes积分和多个ψ-Riemann-Liouville分数阶积分算子.先给出其相应辅助边值问题解的表达式,再利用Banach压缩映像原理和Schaefer不动点定理证明该边值问题解的存在性和唯一性结果,最后举例说明所得结果的有效性.

We considered a class of boundary value problems for fractional differential equations withψ-Caputo fractional derivative,the boundary conditions included a Stieltjes integral and multipleψ-Riemann-Liouville fractional integral operators.Firstly,the expression of solution of corresponding auxiliary boundary value problem was given.Secondly,the existence and uniqueness of solution of the boundary value problem were proved by using Banach compression mapping principle and Schaefer fixed point theorem.Finally,we gave an example to illustrate the validity of the obtained results.