phenomenon. Here we have a new term $R^{\frac{3}{2}}$ in $f(R)$ which can be important for curvature driven inflation. We will discuss more about this term later in the discussion section.

f(R) from New Agegraphic DE model with GUP {#fr-from-new-agegraphic-de-model-with-gup .unnumbered}
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With the corrections due to the generalized uncertainty principle to the entropy area relation we can frame the energy density of the new agegraphic DE model [@f48; @wei6] as $$\label{rho2}
\rho_{\Lambda} = \frac{3n^2~m_p^2}{\eta^2} + \frac{a~m_p}{\eta^3} + \frac{b}{\eta^4}~\ln~(\eta^2~m_p^2) + \frac{c}{\eta^4} ~~,$$ where $\eta$ is the conformal time. $a=b=c=0$ will give back the usual new agegraphic DE model. The parameter $n$ is constrained by present observations and its best fit value is around $2.716_{-0.109}^{+0.111}$ with $1\sigma$ uncertainty [@f56]. The numerical factor $3n^2$ was introduced for a parameterization of some uncertainties such as the effect of curved spacetime (as the K$\acute{a}$rolyh$\acute{a}$zy relation considered only the metric quantum fluctuations of Minkowski spacetime), the species of quantum fields in the universe etc.

For the phantom scale factor the conformal time can be evaluated as $$\eta = \int_t^{t_s}~\frac{dt}{a} = \frac{1}{a_0(h+1)} \left[\frac{6h(2h+1)}{R}\right]^{\frac{h+1}{2}} ~~,~~~~~~~~~~~~h>0 ~~.$$ Substituting this in eqn.(\[rho2\]) we get $$\begin{aligned}
\label{rhap}
\rho_{\Lambda} &= \frac{3~n^2~m_p^2 ~a_0^2 (h+1)^2}{(6h)^{h+1}(2h+1)^{h+1}}~R^{h+1} + \frac{a ~m_p ~a_0^3 (h+1)^3}{(6h)^{\frac{3h+3}{2}}(2h+1)^{\frac{3h+3}{2}}}~R^{\frac{3h+3}{2}} + \nonumber \\
& 