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

R\'egularisation de l'\'equation de Langevin en dimension 1 par le mouvement Brownien fractionnaire