The study aims to present and interpret a novel index based on fractional calculus ( αc) and to assess differences in RR time series dynamics in subjects during meditation. Fractional differintegration (FDI) of a RR time series provides a new time series.αc is defined as the order of the FDI operator that provides the time series with minimum variance. Analyzed time series were obtained from the Exaggerated Heart Rate Oscillations During Two Meditation Techniques database. This database contains RR time series before and after Chi Meditation and Kundalini Yoga. It also contains recordings of elite athletes and healthy subjects while sleeping and during metronomic breathing at 0.25 Hz. αc is significantly higher during Chi or Yoga meditation when compared with the recordings before the meditation starts or in subjects while sleeping or during metronomic breathing.