On the Anomalous Diffusion and the Fractional Generalized Langevin Equations

We introduce the fractional generalized Langevin equation in the absense of a deterministic field, with two deterministic conditions for a particle with unitary mass, i.e., an initial condition and an initial velocity are considered. For a particular correlation function, that characterizes the physical process, and using the methodology of the Laplace transform, we obtain the solution in terms of the three-parameterMittag-Leffler function. As particular cases, some recent resuls are also presented.