In this paper, reconstructing past fractional upper (lower) records from any absolutely
continuous distribution is proposed. For this purpose, two pivotal quantities are given and their exact
distributions are derived. More detailed results, including the case of unknown parameters, are given
for the exponential and Fr ´e chet distributions. Moreover, the exact mean square reconstructor errors
are obtained and some comparisons between the pivotal quantities are performed. To explore the
efficiency of the obtained results, a simulation study is conducted and two real data sets are analyzed