The objective of this work is to develop new modeling and simulation tools for studying strongly coupled plasmas (SCP). Strongly coupled plasmas are different from traditional plasmas as potential energy is larger than the kinetic energy. The standard plasma model does not account for some major effects in SCP: 1) the change in the permittivity 2) the impact on relaxation of the charged particles undergoing Coulomb collisions in a system with weakly shielded long range interactions3) the impact of statistical fluctuations in strongly coupled plasmas that leads to non-Markovian effects. Proper modeling of such systems through consideration of Lévy flight processes gives rise to fractional derivatives in time that result in an incorporation of time history in the model. A Lévy flight is a random walk in which the steps are defined in terms of the step-lengths, which have a certain probability distribution, with the directions of the steps being isotropic and random. Lévy processes in the plasma give rise to fluctuations in medium through which the electromagnetic waves are propagating. Averaging over the Lévy processes will allow us to relate to other important parameters in the plasma.
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