  A multifractal formalism is employed to analyse high-precision time-series
data of \textit{Kepler} stars with surface differential rotation traces. The
multifractal detrended moving average analysis (MFDMA) algorithm has been
explored to characterize the multi-scale behaviour of the observed time series
from a sample of 662 stars selected with parameters close to those of the Sun,
e.g., effective temperature, mass, effective gravity and rotation period. Among
these stars, 141 have surface differential rotation traces, whereas 521 have no
detected differential rotation signatures. In our sample, we also include the
Sun in its active phase. Our results can be summarized in two points: first,
our work suggests that starspots for time series with and without differential
rotation have distinct dynamics, and second, the magnetic fields of active
stars are apparently governed by two mechanisms with different levels of
complexity for fluctuations. Throughout the course of the study, we identified
an overall trend whereby the differential rotation is distributed in two $H$
regimes segregated by the degree of asymmetry $A$, where $H$-index denotes the
global Hurst exponent which is used as a measure of long-term memory of time
series. As a result, we show that the degree of asymmetry can be considered a
segregation factor that distinguishes the differential rotation behaviour when
related to the effect of the rotational modulation on the time series. In
summary, the multifractality signals in our sample are the result of magnetic
activity control mechanisms leading to activity-related long-term persistent
signatures.
