  Very recently Ali et al.(2009) proposed a new generalized uncertainty
principle (or GUP) with a linear term in Plank length which is consistent with
doubly special relativity and string theory. The classical and quantum effects
of this generalized uncertainty principle (term as modified uncertainty
principle or MUP) are investigated on the phase space of a dilatonic
cosmological model with an exponential dilaton potential in a flat FRW
background . Interestingly, as a consequence of MUP, we found that it is
possible to get a late time acceleration for this model. For the quantum
mechanical description in both commutative and MUP framework, we found the
analytical solutions of the Wheeler-DeWitt equation for the early universe and
compare our results. We have used an approximation method in the case of MUP.
