含左右分数导数的时滞微分方程解的存在性和唯一性

Existence and uniqueness of solutions for delay differential equations with left and right fractional derivatives

研究了一类含左右Caputo分数导数的时滞微分方程Riemann-Stieltjes积分边值问题。通过构建单调迭代序列并利用上下解方法得到了边值问题解的存在性与唯一性定理。最后给出实例以说明本文的主要结论的适用性。

A class of Riemann-Stieltjes integral boundary value problems for delay differential equations with Caputo left and right fractional derivatives was studied.The existence and uniqueness of solutions for the boundary value problems were obtained by constructing the monotone iterative sequences and using the method of upper and lower solutions.Finally,an example was given to illustrate the main conclusions.