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

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.