The light curves of solar-like stars can exhibit rotational modulation due to dark spots co-rotating with the stellar surface. In addition to constraints on rotation properties, rotational modulation can also provide details on stellar magnetic activity. In this work, we investigate the temporal variation of the photometric magnetic activity proxy, Sph, of Kepler solar-like stars. We find that stars on average photometrically more active are also more variable in time, independently of spectral type. This relationship was known for the chromospheric activity index, but here we show that Kepler photometric data show a similar behavior. There is an additional dependency of the Sph variation on the rotation period, even after correcting for the dependencies on different stellar parameters. Furthermore, we compare the Sun with Kepler Sun-like stars, selected according to the recent Gaia-Kepler stellar properties catalog and the recent rotation catalog for Kepler solar-like stars. While, depending on the phase of the cycle, the Sun is among the less active stars, we find that the behavior of the magnetic activity proxy for the Sun is consistent and normal in comparison with that observed in Kepler Sun-like stars. In order to have a more complete picture of the stellar magnetic activity, long-term observations are important. In addition, using synthetic data, we also investigated lifetimes of active regions and found that the observational length is also a crucial parameter in the context of constraining lifetimes of active regions. These analyses may help us to improve the understanding solar and stellar magnetism and its associated timescales.

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