  We consider a large scale environment of turbulent reconnection that is
fragmented into a number of randomly distributed Unstable Current Sheets (UCS),
and we statistically analyze the acceleration of particles within this
environment. We address two important cases of acceleration mechanisms when the
particles interact with the UCS: (a) electric field acceleration, and (b)
acceleration through reflection at contracting islands. Electrons and ions are
accelerated very efficiently, attaining an energy distribution of power-law
shape with an index $1-2$, depending on the acceleration mechanism. The
transport coefficients in energy space are estimated from the test-particle
simulation data, and we show that the classical Fokker-Planck (FP) equation
fails to reproduce the simulation results when the transport coefficients are
inserted into it and it is solved numerically. The cause for this failure is
that the particles perform Levy flights in energy space, the distributions of
energy increments exhibit power-law tails. We then use the fractional transport
equation (FTE) derived by Isliker et al., 2017, whose parameters and the order
of the fractional derivatives are inferred from the simulation data, and,
solving the FTE numerically, we show that the FTE successfully reproduces the
kinetic energy distribution of the test-particles. We discuss in detail the
analysis of the simulation data and the criteria that allow judging the
appropriateness of either an FTE or a classical FP equation as a transport
model.
