Numerical algorithms for nonlinear fractional stochastic Volterra-type equation

Abstract

In this work, we investigate a class of nonlinear stochastic Volterra-type evolution equations, which can be regarded as an extension of the results reported in Qiao et al. (Fract Calc Appl Anal 27:1136–1161, 2024). For such equations, we propose an Euler scheme and rigorously establish the existence, uniqueness, and regularity of the solution. Moreover, we present the detailed numerical implementation of the scheme and derive the corresponding error estimates.