The Dyson-Brownian motion is the process of eigenvalues of a matrix Brownian motion. The limiting of its empirical spectral process, when dimension increases, is the free Brownian motion (frBm), a measure valued process that is the law of a non commutative process. In this talk we present two new non commutative processes arising in a similar way as the frBm, from fractional Hermitian Brownian...