Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically

The current study pursues the specific goal of determining the approximate solution of the linear stochastic fractional Itô-Volterra integral equations which has been caused by fractional Brownian motion under Hurst parameter $0 < H< 1$ , using a numerical approach. The obtained results are based on a stochastic operational matrix of integration on generalized block-pulse basis function. In fact, we transform the equation to a linear system of algebraic equations via a lower triangular coefficients matrix from the equation, and get an approximation solution with accuracy of order $O(h^{2})$ by solving it. Then the error analysis is revealed by some theorems and definitions. Finally, an application exhibits applicability and accuracy of the method numerical.