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.