The study is carried out within the framework of a fractional model of the deformation process in a seismically active region. The compound Poisson power-law process in a fractional time representation is considered as a model. The probabilistic characteristics of this process are expressed by the Mittag-Leffler function with a power-law argument, which takes into account the power-law frequency distribution of events. To verify the model, data from the earthquake catalog of the Kamchatka Branch of the Federal Research Center ”Geophysical Survey of the Russian Academy of Sciences” (KB FRC GS RAS) for the period from 1 January 1962 to 31 December 2002 for the subduction zone of the Kuril-Kamchatka Island arc are used. The calculation of the empirical Cumulative Distribution Function (eCDF) of foreshocks and aftershocks is carried out on the basis of two algorithms, the first of which considers events that correlate only with the mainshock based on the accepted criteria of spatial, time and energy connectivity of events. The second algorithm takes into account the branching of the process, considering events statistically related to both the mainshock and those related to the main one. The eCDF are approximated by the three-parameter Mittag-Leffler function. The values of the fractional parameters characterize the properties of the hereditary and non-stationary of the deformation process in a seismically active region. The values of the fractional parameters calculated of the eCDF of the forshocks and aftershocks using two algorithms are compared and conclusions are drawn about the influence of the class of the mainshock on their values. The work was supported by IKIR FEB RAS State Task (subject registration  124012300245-2).