Spectral method for solving linear Caputo fractional stochastic differential equations

Abstract

Abstract We concern on the problem of finding the solution to the linear Caputo fractional stochastic differential equation with additive and multiplicative noise. It is proposed to apply the spectral method based on the spectral form of mathematical description. This method provides both an explicit form of the solution as the orthogonal series with random coefficients and a continuous-time approximation of this solution as the partial sum. Earlier, the spectral method has been applied for solving linear (non-fractional) stochastic differential equations. The proposed method is demonstrated on the modeling fractional Ornstein– Uhlenbeck process described by a linear Caputo fractional stochastic differential equation with additive noise.