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The cosmological reconstruction of modified $F(R)$ and $F(\mathcal{G})$gravities with agegraphic dark energy (ADE) model in a spatially flat universewithout matter field is investigated by using e-folding "$N$" as a forward way.After calculating a consistent $F(R)$ in ADE's framework, we obtain conditionsfor effective equation of state parameter $w_{\mathrm{eff}}$, and see thatreconstruction is possible for both phantom and non-phantom era. Thesecalculations also are done for $F(\mathcal{G})$ gravity and the condition for aconsistent reconstruction is obtained.

Agegraphic reconstruction of modified $F(R)$ and $F(\mathcal{G})$ gravities