This paper discusses some properties of solutions to fractional neutral delay differential equations. By combining a new weighted norm, the Banach fixed point theorem and an elegant technique for extending solutions, results on existence, uniqueness, and growth rate of global solutions under a mild Lipschitz continuous condition of the vector field are first established. Be means of the Laplace transform the solution of some delay fractional neutral differential equations are derived in terms of three-parameter Mittag–Leffler functions; their stability properties are hence studied by using use Rouché’s theorem to describe the position of poles of the characteristic polynomials and the final value theorem to detect the asymptotic behavior. By means of numerical simulations the theoretical findings on the asymptotic behavior are verified.

本文讨论分数阶中立型时滞微分方程解的一些性质。通过结合一个新的加权范数，Banach不动点定理和一种扩展解的优雅技术，首先确定了在矢量场的温和Lipschitz连续条件下整体解的存在性，唯一性和增长率的结果。通过拉普拉斯变换，根据三参数Mittag-Leffler函数推导了一些时滞分数中立型微分方程的解；因此，通过使用Rouché定理描述特征多项式极点的位置以及检测渐近行为的最终值定理，研究了它们的稳定性。通过数值模拟，验证了关于渐近行为的理论发现。