This manuscript examines the problem of nonlinear stochastic fractional neutral integro-differential equations with weakly singular kernels. Our focus is on obtaining precise estimates to cover all possible cases of Abel-type singular kernels. Initially, we establish the existence, uniqueness, and continuous dependence on the initial value of the true solution, assuming a local Lipschitz condition and linear growth condition. Additionally, we develop the Euler-Maruyama method for the numerical solution of the equation and prove its strong convergence under the same conditions as the well-posedness. Moreover, we determine the accurate convergence rate of this method under global Lipschitz conditions and linear growth conditions.

翻译：本文研究具有弱奇异核的非线性随机分数阶中立型积分微分方程问题。重点在于获取涵盖所有阿贝尔型奇异核情形的精确估计。首先，在局部Lipschitz条件和线性增长条件下，建立真解的存在性、唯一性以及对初值的连续依赖性。此外，我们发展该方程的数值求解Euler-Maruyama方法，并在与适定性相同条件下证明其强收敛性。进一步地，在全局Lipschitz条件和线性增长条件下，确定该方法的精确收敛速率。