An integro quadratic spline-based scheme for solving nonlinear fractional stochastic differential equations with constant time delay

•Nonlinear fractional stochastic differential equations with constant time delay is under consideration.•A new computational scheme based on a piecewise integro quadratic spline interpolation is proposed.•The convergence properties of the scheme are investigated.•The accuracy of the proposed scheme is analyzed in the perspective of the expected mean absolute norm error and experimental convergence order.•1he statistical indicators are analyzed for assessing the performance of the proposed scheme. This paper proposes an accurate and computationally efficient technique for the approximate solution of a rich class of fractional stochastic differential equations with constant delay driven by Brownian motion. In this regard, a piecewise integro quadratic spline interpolation approach is adopted for approximating the fractional-order integral. The performance of the computational scheme is evaluated by statistical indicators of the exact solutions. Moreover, the computational convergence is also analysed. Three families of models with stochastic excitations illustrate the accuracy of the new approach as compared with the M-scheme.