  In this study, we report on the analysis of 701 stars in a solar vicinity
defined in three categories namely subsolar, solar, and supersolar with
rotation periods between 1 and 70 days, based on rotational modulation
signatures inferred from time series from the Kepler mission's Public Archives.
In our analysis, we performed an initial selection based on the rotation period
and position in the period-H diagram, where H denotes the Hurst exponent
extracted from fractal analysis. To refine our analysis, we applied a fractal
approach known as the R/S method, taking into account the fluctuations of the
features associated with photometric modulation at different time intervals and
the fractality traces that are present in the time series of our sample. In
this sense, we computed the so-called Hurst exponent for the referred stars and
found that it can provide a strong discriminant of rotational modulation and
background noise behavior, going beyond what can be achieved with solely the
rotation period itself. Furthermore, our results emphasize that the rotation
period of stars is scaled by the exponent H which increases following the
increase in the rotation period. Finally, our approach suggests that the
referred exponent may be a powerful rotational modulation and noise classifier.
