From solar flare time series to fractional dynamics

We demonstrate that continuous-time FARIMA processes with alpha-stable noise provide a new stochastic tool for studying the solar flare phenomenon in the framework of fractional Langevin equation. Simple computer tests to check the origins of alpha-stability and self-similarity are implemented for empirical time series describing the energy of solar flares. Based on observed physical time series we solve the challenging problem of how to detect long-range dependence from real data and how to model it via fractional dynamics (Langevin or Fokker-Planck). We employ here codifference as a proper measure for long-range dependence. It is applicable to empirical data from the distribution lacking the second moment.