The motion of Brownian particles described by the generalized Langevin equation (GLE) is studied. The molecular dynamics (MD) simulations of simple Brownian particles with various masses and diameters are performed. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force are determined and their dependence on mass and diameter are investigated. The friction coefficient of the particle is derived from integral of the memory function. In two-dimensional system, the normal diffusion conditions in which the friction coefficient is defined are related to order-disorder transiton. Integral of the short time region of memory functions is estimated by Enskog`s theoretical friction coefficient. In two-dimensional confined fluid between parallel walls, friction coefficients and diffusivities are defined even at low-density systems. It is also observed that the transport of Brownian particles in confined non-equilibrium fluid in which the external force is acting on the Brownian particle only.