We analyze a possible superconductivity in the hole-doped system of layeredhydrogenized graphene by taking into account thermal fluctuations of the orderparameter. In particular, we demonstrate that in the one-layer case the valuesof the high mean-field (MF) critical temperature $T_{c}^{MF}\sim 80-90K$,predicted recently by Savini et al \cite{Savini}, do not alter significantlydue to the fluctuations, and the Berezinskii-Kosterlitz-Thouless (BKT) criticaltemperature of the vortex superconductivity is almost the same as the MFtemperature at doping 0.01-0.1. We show that in the case of multilayer system,when the coupling between the layers stabilizes the superconducting phase inthe form of fluxon superconductivity, the critical temperature $T_{c}$ canincrease dramatically to the values $\sim 150K$, higher than the correspondingvalues in cuprates under ambient pressure.
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