Numerical method for solving linear stochastic It(o)over-cap-Volterra integral equations driven by fractional Brownian motion using hat functions

In this paper, we present a numerical method to approximate the solution of linear stochastic Ito-Volterra integral equations driven by fractional Brownian motion with Hurst parameter H is an element of(0, 1) based on a stochastic operational matrix of integration for generalized hat basis functions. We obtain a linear system of algebraic equations with a lower triangular coefficients matrix from the linear stochastic integral equation, and by solving it we get an approximation solution with accuracy of order O(h(2)). This numerical method shows that results are more accurate than the block pulse functions method where the rate of convergence is O(h). Finally, we investigate error analysis and with some examples indicate the efficiency of the method.