非线性项具有积分算子的分数阶反周期边值问题解的存在性与唯一性

摘要

A nonlinear fractional anti-periodic boundary problem was considered, the differential operator of which is the Caputo sense of order 2<α≤3.The feature of this problem is that nonlinear term contains integral operators about unknown function.The existence and uniqueness of solution were proved via the Schauder fixed point theorem and the contraction mapping principle.%考虑一个非线性项中含有关于未知函数的积分算子的非线性分数阶的反周期边值问题，其导数类型为 Caputo 型分数阶导数，阶数为2<α≤3.应用 Schauder 不动点定理和压缩映象原理证明了该问题解的存在性与唯一性.