Innovative computational model for variable order fractional Brownian motion and solving stochastic differential equations

This paper presents an efficient computational method based on barycentric rational interpolants for solving a novel class of nonlinear stochastic differential equations driven by variable order fractional Brownian motion. The method approximates the solution using barycentric rational interpolants, transforming the problem into a system of nonlinear algebraic equations. Its convergence is rigorously analyzed, demonstrating theoretical soundness. Numerical experiments confirm the method's reliability and versatility across various stochastic models. Additionally, a novel procedure for approximating the value of variable order fractional Brownian motion at arbitrary points is introduced, utilizing a straightforward matrix algorithm based on block pulse functions. This algorithm simplifies the approximation of variable order fractional Brownian motion, providing a computationally efficient and practical solution.