In this paper, a new class of a neutral functional delay differential equation involving the generalized -Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results.

中文翻译：

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具有广义Caputo算子的中性泛函时滞微分方程的一些定性分析

在本文中，一类新的中性官能延迟微分方程涉及广义-卡普托衍生物上的部分有序的Banach空间调查。借助Dhage技术和Banach收缩原理，建立了给定边值问题的存在唯一性结果。此外，我们还通过拓扑度方法证明了其他存在标准。最后，研究了 Ulam-Hyers 类型稳定性及其广义版本。提供了两个说明性示例来证明我们获得的结果的有效性。