Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel
Numerical Analysis
2025-04-18 v2 Numerical Analysis
Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.2401.15407,
title = {Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel},
author = {Javad A. Asadzade and Nazim I. Mahmudov},
journal= {arXiv preprint arXiv:2401.15407},
year = {2025}
}