  The main goal of this paper is to provide a fractional stochastic
differential equation modelling the physical phenomena governed by the Langevin
equation in 1-dimension. A generalized equation leaning on the fractional
Brownian motion (fBm) will be proposed, the later will allow a description of
the complexity of the physical systems which escape any prediction of the of
the standard Langevin equation. We shall begin at first to remind the basic
notions of the standard Brownian motion (Bm) and the fractional Brownian motion
(fBm), then, we shall establish a generalization to long memory of the Langevin
equation.
