  This paper further discusses the tempered fractional Brownian motion, its
ergodicity, and the derivation of the corresponding Fokker-Planck equation.
Then we introduce the generalized Langevin equation with the tempered
fractional Gaussian noise for a free particle, called tempered fractional
Langevin equation (tfLe). While the tempered fractional Brownian motion
displays localization diffusion for the long time limit and for the short time
its mean squared displacement has the asymptotic form $t^{2H}$, we show that
the asymptotic form of the mean squared displacement of the tfLe transits from
$t^2$ (ballistic diffusion for short time) to $t^{2-2H}$, and then to $t^2$
(again ballistic diffusion for long time). On the other hand, the overdamped
tfLe has the transition of the diffusion type from $t^{2-2H}$ to $t^2$
(ballistic diffusion). The tfLe with harmonic potential is also considered.
