  We study the effect of Chandrasekhar and Holstmark's distribution of field
fluctuations on the dynamics of N-body systems interacting via Coulomb or
Newton gravitational force. We develop an approach based on statistical
dynamics first principles whose mathematical framework is similar to the one
used by Chandrasekhar and Holstmark for their field fluctuation theory. We use
the Picard iteration method to approximate the Hamiltonian dynamics in the
short time limit. Neglecting correlations between particles, carrying the
thermodynamic limit and assuming that the system is spatially homogeneous, we
find a fractional kinetic equation for the velocity distribution. Both, the
fractional derivative order and the asymptotic behavior of the solution appear
to be directly connected to the $1/r^2$ behavior of the Coulombian or
gravitational interaction force over short distances.
