For our purpose we need to solve eqn.(\[maineq\]) and we borrow the energy density from the holographic and agegraphic dark energy models respectively.

Considering the leading order terms of eqn.(\[ent\]) and following the arguments of [@f48; @wei6] we can write the GUP motivated energy density for the holographic DE model as $$\label{hd}
\rho_{\Lambda} = \frac{3n^2 m_p^2}{L^2} + \frac{a m_p}{L^3} + \frac{b}{L^4} \ln(L^2 m_p^2) + \frac{c}{L^4} ~~.$$ Here $n,a,b$ and $c$ are constants and $L$ is the future event horizon. If $a=b=c=0$ we get the usual holographic DE model. Though $n$ is a constant but its value can be constrained from the latest observational data [@f97]. The future event horizon is defined as $$L = a \int_t^{\infty} \frac{d t}{a} ~~.$$ For the phantom scale factor the future event horizon is $$L = a \int_t^{t_s} \frac{d t}{a} = \frac{1}{h+1} \sqrt{\frac{6h(2h+1)}{R}}$$ Putting the value of $L$ in eqn.(\[hd\]) we get the form of energy density as $$\label{rhoh}
\rho_{\Lambda} = \frac{3n^2 m_p^2 (h+1)^2}{6h(2h+1)}R + \frac{a m_p (h+1)^3}{(6h)^{\frac{3}{2}}(2h+1)^{\frac{3}{2}}} R^{\frac{3}{2}} + \frac{(h+1)^4 R^2}{(6h)^2(2h+1)^2}\left[b\ln\left\{\frac{6h(2h+1) m_p^2}{(h+1)^2 R} \right\} + c \right] ~~.$$ Now eqn.(\[maineq\]) can be written in terms of $R$ as $$\begin{aligned}
R^2 f''(R) &- \frac{(h+1)}{2}Rf'(R) + \frac{(2h+1)}{2}f(R) = -\frac{n^2 (h+1)^2}{2h}R  -\frac{a}{m_p} \frac{(h+1)^3}{(6h)^{\frac{3}{2}}(2h+1)^{\frac{1}{2}}} R^{\frac{3}{2}} \nonumber \\
&+ 