explanation of the very early inflation along with presently observed late time acceleration. We considered the generalized uncertainty principle in our approach which incorporated the corrections in the entropy area relation which thereby modified the energy densities for the cosmological DE models considered here [^4]. We found that the GUP motivated holographic and new agegraphic $f(R)$ gravity models can behave like phantom or quintessence models in the spatially flat FRW universe. A similar study was also carried out by authors in [@f]. We reproduced all the result and conclusion of [@f] but in addition we also found a distinct term in the form of $f(R)$ which goes as $R^{\frac{3}{2}}$ due to the consideration of the GUP modified energy densities. This is really very interesting if we consider the phenomenological consequence of our study. Although the presence of this term in the action can have its importance for inflation but Capozziello [*et.al.*]{} [@capo1; @capo2] introduced an action with $f(R) \sim R^m$ and showed that it leads to an accelerated expansion, [*i.e.*]{}, a negative value for the deceleration parameter $q$ for $m \approx \frac{3}{2}$ which fit well with SNeIa and WMAP data. Apart from the $R^{\frac{3}{2}}$ term we also found the other 