& - 2\delta (1-h-r) ~R_0^h - 2\gamma (2 - 2h-r) ~R_0 ~\ln ~[R_0^{1-h}] \big]\end{aligned}$$ and $$\begin{aligned}
C_2 =& \frac{R_0^{1-2h-r}}{2(r-q)} \big[4q~R_0^{2h} - \alpha (3 -3h-2q) ~R_0^{\frac{h+1}{2}} - 2(2\beta -2h\beta - q\beta +\gamma -h\gamma) ~R_0 \nonumber \\
& - 2\delta (1-h-q) ~R_0^h - 2\gamma (2 - 2h-q) ~R_0 ~\ln ~[R_0^{1-h}] \big] ~~.\end{aligned}$$ For the scale factor $a(t) = a_0~e^{Ht}$ with $H=constant$ (deSitter) we write the conformal time as $$\label{last1}
\eta = \int_0^{\infty} \frac{dt}{a} = \frac{1}{a_0H} = \sqrt{\frac{12}{a_0^2~R}} ~~.$$ Here we have set the upper limit of the integration to $t\rightarrow \infty$ to express $\eta$ in terms of $R$. The relevant modification to the energy density (\[rho2\]) will be $$\label{last2}
\rho_{\Lambda} = \frac{3~n^2~m_p^2}{\eta^2} + \frac{a~m_p}{\eta^3} + \frac{b}{\eta^4} \ln~(\eta^2~m_p^2) + \frac{c}{\eta^4} ~~.$$ The solution of eqn.(\[maineq\]) with (\[last1\]) and (\[last2\]) yields the form of $f(R)$ as $$f(R) = -n~a_0^2~R + C_1~R^2 - \frac{a~a_0^3}{3\sqrt{3}m_p}~R^{\frac{3}{2}} - \frac{b~a_0^4}{72~m_p^2}~R^2~\left[\ln \left(\frac{12~m_p^2}{a_0~R}\right)\right]^2  + \frac{c~a_0^4}{36~m_p^2}~R^2~\ln[R]~~.$$ where $C_1$ is the integration constant to be fixed with boundary conditions. Here also like the holographic DE model we have a new term $R^{\frac{3}{2}}$ in $f(R)$ which can be important for curvature driven inflation.

Discussion {#discussion .unnumbered}
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In this study we considered the generalized uncertainty principle motivated forms of the holographic and the new 