In view of applications to electron-positron pair-plasmas and fullerene
pair-ion-plasmas containing charged dust impurities a thorough discussion is
given of three-component Plasmas. Space-time responses of multi-component
linearized Vlasov plasmas on the basis of multiple integral equations are
invoked. An initial-value problem for Vlasov-Poisson -Ampere equations is
reduced to the one multiple integral equation and the solution is expressed in
terms of forcing function and its space-time convolution with the resolvent
kernel. The forcing function is responsible for the initial disturbance and the
resolvent is responsible for the equilibrium velocity distributions of plasma
species. By use of resolvent equations, time-reversibility, space-reflexivity
and the other symmetries are revealed. The symmetries carry on physical
properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing
equilibrium distributions for dusty pair plasmas, we can reduce the resolvent
equation to: (i) the undamped dispersive wave equations, (ii) wave-diffusive
transport equation (iii) and diffusive transport equations of oscillations. In
the last case we have to do with anomalous diffusion employing fractional
derivatives in time and space. Fractional diffusion equations account for
typical anomalous features, which are observed in many systems, e.g. in the
case of dispersive transport in amorphous semiconductors, liquid crystals,
polymers, proteins and biosystems.Comment: 6 page
