A numerical approach based on Pell polynomial for solving stochastic fractional differential equations

In this article, Pell operational matrix method is discussed to solve the stochastic fractional differential equation. For that purpose, the Pell polynomial is considered as a basis function. The operational matrices, such as the product operational matrix, the integral operational matrix, the operational matrix for fractional integration, and the stochastic operational matrix, are described in detail. Further suitable collocation points are used to convert the stochastic fractional differential equation into a system of algebraic equations. Finally, Newton’s method is applied to solve them. The convergence and error analysis has been discussed in detail. The reliability and efficiency of the proposed method are described by some illustrative examples. The accuracy of the Pell operational matrix method is demonstrated by comparing its results with the numerical solutions of the cubic B-spline collocation method, linear cardinal B-spline operational matrix method, and shifted Jacobi operational matrix method.