Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme

Abstract

In this article, a step-by-step collocation approach based on the shifted Legendre polynomials is presented to solve a fractional order system of nonlinear stochastic differential equations involving a constant delay. The problem is considered with suitable initial condition and the fractional derivative is in the Caputo sense. With a step-by-step process, first, the considered problem is converted into a non-delay fractional order system of nonlinear stochastic differential equations in each step and then, a shifted Legendre collocation scheme is introduced to solve this system. By collocating the obtained residual at the shifted Legendre points, we get a nonlinear system of equations in each step. The convergence analysis and rate of convergence of the proposed method are investigated . Finally, three test examples are provided to affirm the accuracy of this technique in the presence of different noise measures.