Numerical Solution of Persistent Processes Based Fractional Stochastic Differential Equations

This paper proposes the shifted Legendre polynomial approximations-based stochastic operational matrix of integration method to solve persistent processes-based fractional stochastic differential equations. The operational matrix of integration, stochastic operation matrix and fractional stochastic operational matrix of the shifted Legendre polynomials are derived. The stochastic differential equation is transformed into an algebraic system of (N + 1) equations by the operational matrices. For the proposed approach, a thorough discussion of the error analysis in L-2 norm is provided. The proposed method's applicability, correctness, and accuracy are examined using a few numerical examples. Comparing the numerical examples to the other methods discussed in the literature demonstrates the solution's effectiveness and attests to the solution's high quality. The error analysis also reveals the method's superiority. A more accurate solution is obtained, thus maintaining a minimum error.