An Effective Wavelet Approach to Solve Nonlinear Sdes Driven by Multi-Fractional Gaussian Noise

The objective of this research is to develop a novel and efficient approach by using Legendre wavelets to approximate solutions of nonlinear stochastic differential equations (SDEs) driven by multi-fractional Gaussian noise (MFGN). Consequently, based on these wavelets, we derive a stochastic operational matrix of integral (OMI) with respect to the multi-fractional Brownian motion (MFBM) and an exact operational vector of integral (OVI). Then, we employ them to provide approximate solutions for the mentioned problems. Additionally, we analyze the convergence of our approach. Furthermore, we solve four test problems and present comparisons between our results and those of the existing numerical methods to validate the advantages of our method.