Numerical solution for a class of time-fractional stochastic delay differential equation with fractional Brownian motion

In this article, a numerical scheme is proposed to solve a class of time-fractional stochastic delay differential equations (TFSDDEs) with fractional Brownian motion (fBm). First, we convert the TFSDDE into a non-delay equation by using a step-by-step scheme. Then, by applying a collocation method based on Jacobi polynomials (JPs) in each step, the non-delay equation is reduced to a  nonlinear system of algebraic equations. The convergence analysis of the presented scheme is evaluated. Finally, two numerical test examples are presented to highlight the applicability and efficiency of the investigated method.