C. α ∈ (1 , 2) and and Thus, since α ∈ (1 , 2), the transport of particles is superdiffusive. Interestingly, depending on the exponent α , the increase of the particle mass µ can either enhance or suppress the biased diffusion. In order to show this, we first use Eq. (3.1) with m = 1 to represent the mean waiting time τ in the form as t → ∞ . Accordingly, the long-time behavior of the variance σ $^{2}$( t ) is described by the power law as s → 0, and the straightforward calculation of the Laplace transforms (4.8) yields Proceeding in the same way as before, we obtain Since in this case lim$_{t}$ →∞ 〈 Y$_{t}$ 〉 $^{2}$/ 〈 Y 2 t 〉 = 1 (see below), for finding the long-time behavior of σ $^{2}$( t ) we should determine the first two terms of the asymptotic expansion of 〈 Y$_{t}$ 〉 and 〈 Y 2 t 〉 as t → ∞ . To this end, taking into account that at α ∈ (1 , 2) the mean waiting time τ = ∫ ∞ τ$_{min}$ dτ τ p ( τ ) exists, we use the following formula: ∞ 12 p$_{s}$ = 1 − τ s − ∫ τ$_{min}$ dτ (1 − sτ − e − $^{sτ}$) p ( τ ) . (4.14) p$_{s}$ − 1 + τ s ∼ a Γ(2 − α ) α ( α 1) s α (4.15) 〈 Y$_{t}$ 〉 s − l τ 1 s 2 ∼ la Γ(2 − α ) τ $^{2}$α ( α 1) 1 s 3 − α (4.16) 〈 Y 2 t 〉 s − 2 l 2 τ 2 1 s 3 ∼ 4 l $^{2}$a Γ(2 − α ) τ $^{3}$α ( α 1) 1 s 4 − $_{α}$. (4.17) 〈 Y$_{t}$ 〉 − τ t ∼ τ $^{2}$α ( α − 1)(2 − α ) t 2 − α (4.18) 〈 Y 2 t 〉 − l 2 τ 2 t 2 ∼ 4 l $^{2}$a τ $^{3}$α ( α − 1)(2 − α )(3 − α ) t 3 − α (4.19) σ $^{2}$( t ) ∼ 2 l $^{2}$a τ $^{3}$α (2 − α )(3 − α ) t 3 − $^{α}$. (4.20) τ = τ$_{od}$ ( 1 + 1 κτ$_{od}$ − g$_{0}$ κνl ) , (4.21) These asymptotic formulas are particular cases of the asymptotic formula (4.3) with L (1 /s ) = const. Therefore, using the well-known property of the gamma function, Γ(1+ x ) = x Γ( x ), from (4.4) we get