| Summary: | Using a generalized function of the stellar spin-down law, we investigate the dependence of the magnetic braking index on the age of different clusters. Initially, our research consists of 14 open clusters with age less than 1 Gigayear and ranging in mass from 0.7 to 1.4 $M_{\odot}$ distributed in three subsamples. We also used $6$ open clusters and $1$ globular cluster with ages greater than 1 Gigayear. Our objective is to verify the temporal behavior of the non-extensive braking index $q$ which brings the cumulative distribution of the rotational velocities of the stars of the youngest cluster $X$ taken at the future age of an older cluster denoted by $Y$. As a result, the $q$ -index is calculated over time $t_{Y}-t_{X}$, where $t_{Y}$ denotes the age of the oldest open cluster used to estimate the future cumulative distribution of the rotation velocity of the cluster $X$ with the current age $t_{X}$. Our results indicate that for clusters younger than $1$ Gigayear, the values of $q$ are slightly constant. For clusters older than $1$ Gigayear, the results found for the temporal evolution of the magnetic brake index also showed a smoothly constant behavior for the values of $q$. The results also indicate a decrease in stellar rotation caused by the deceleration of the magnetic brake index.
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