Abstract
In this article, a discussion about stochastic integral equations driven by multi-fractional Gaussian (MFGN) noise has been done which determines the stochastic solutions to fundamental equations to the study of diffusion dynamics in vibrated granular systems. A Bernstein polynomials (BP) approach has been implemented to find an approximation of the stochastic integral equations under study which is efficient and has less computational cost. An example based on the integral equation has been solved to further more establish the efficiency of the polynomial scheme.
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