Numerical Solution for a Class of Time-Fractional Stochastic Delay Differential Equations with Fractional Brownian Motion

In this article, a numerical scheme is proposed to solve a class of time-fractional stochastic delay differential equations (TFSD- DEs) 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 sys- tem of algebraic equations. The convergence analysis of the presented scheme is evaluated. Finally, two numerical test examples are presented to highlight the applicability and effciency of the investigated method. .