A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise

Highlights：

• A novel approach is presented to obtain and analyze the behavior of numerical solutions of nonlinear stochastic differential equations driven by multifractional Gaussian noise.

• For the first time, based on the generalized hat functions, a formula for the operational matrix of the integral operator with respect to the fractional variable-order Brownian motion is derived.

• Converting different problems into a system of equations by using this operation matrix.

• Convergence of the new method is theoretically analyzed.

• The efficiency of the new method is confirmed by solving stochastic logistic equation, stochastic population growth model, and three test problems.

• The presented method is an efficient numerical tool for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise.