light of the generalized uncertainty principle [^2]. We will use eqn. (\[ent\]) to calculate the energy density for the models. Later we will construct the form of $f(R)$ and the equation of state parameter $\omega$ for each of these DE models. Although an earlier attempt is present in the literature for the reconstruction of $f(R)$ [@f] but we will later conclude with a brief comparison of the results.

f(R) from Holographic DE model with GUP {#fr-from-holographic-de-model-with-gup .unnumbered}
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In $f(R)$ gravity the action is written as [@sud59; @sud60; @sud61] $$S = \int \sqrt{-g}~ d^4x \left(\frac{R+f(R)}{16\pi G} + L_{matter}\right) ~~.$$ The considerations lies in the fact that the higher order modifications of the Ricci curvature $R$ in the form of $R^2$ or $R_{\mu \nu}R^{\mu \nu}$ could give rise to inflation at the very early universe [^3]. So this lead to a notion that whether inverse powers in $R$ dominant in late time universe can give an explanation to the recent predicted acceleration of the universe. But this type of models face problems of stability [@sud11]. The variation of the action with respect to the metric gives the field equations as $$R_{\mu \nu} - \frac{1}{2}R g_{\mu \nu} = 8 \pi G \left(T_{\mu 