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Fourier spectral methods for solving some linear stochastic space-fractional partial differential\udequations perturbed by space-time white noises in one-dimensional case are introduced and analyzed.\udThe space-fractional derivative is defined by using the eigenvalues and eigenfunctions of Laplacian subject\udto some boundary conditions. We approximate the space-time white noise by using piecewise constant\udfunctions and obtain the approximated stochastic space-fractional partial differential equations. The\udapproximated stochastic space-fractional partial differential equations are then solved by using Fourier\udspectral methods. Error estimates in $L^{2}$- norm are obtained. Numerical examples are given

Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations