A kinetic formulation is developed to investigate low-frequency dust ion acoustic waves (DIAWs) and dust acoustic waves (DAWs) as well as numerically for a four-component, collisionless, unmagnetized dusty plasma, using the linearized Vlasov-Poisson model for species obeying the Maxwellian distribution. In particular, the dynamics of low-frequency DIAWs is investigated by considering two cases. In the first case, ions and positive dust particles are assumed to be dynamically adiabatic while the negative dust particles are static in the background. In second case, the ions are taken adiabatic, while both positive and negative dust particles are static in the background. For DAWs, the ions are assumed to be isothermal, while both positive and negative dust species are considered adiabatic. Electrons are assumed to be isothermal in all cases. The linear characteristics and Landau damping rates for DIAWs and DAWs are investigated with effects of the dust particle concentrations and different temperature ratios. It is noted that for higher values of positive dust concentration, DIAWs (DAWs) are less (more) damped. It is also observed that the damping rate increases (decreases) as T i approaches T e for DIAWs (DAWs). It is worth adding here that the theoretical results presented here are supported by numerical analyses and illustrations. The relevance of the study to laboratory and cosmic plasmas is also pointed out. KEYWORDSacoustic waves, dusty plasma, kinetic theory, Landau damping, longitudinal response function INTRODUCTIONA great deal of interest has been shown in the study of dusty plasmas in the last few decades with a view to understanding the propagation of linear and non-linear excitations. Dusty plasmas are very abundant and exist in the laboratory [1,2] as well as in space and astrophysical surroundings [3][4][5][6] such as cometary tails, planetary rings, and the interstellar medium. The existence of a high density of dust grains in a plasma system causes the generation of some complex and collective processes that introduce several new modes, for example, dust acoustic waves (DAWs), [7] dust lattice waves (DLWs), [8,9] , dust drift waves (DDWs), and dust ion acoustic waves (DIAWs).[10] Earlier investigations had been carried out to study the most common dusty plasma system consisting of negative dust particles, ions, and electrons. [7][8][9][10] The main reason for considering the negative dust grain is the fundamental process of charging, that is, the collection of particles with high thermal energy, namely electrons, by the dust grain. However, some new charging mechanisms have been investigated due to which the dust grain can be charged positively. These charging mechanisms are (a) photoemission in the presence of ultraviolet (UV) photons, [11,12] (b) thermionic emission caused by radiative heating, [13] and (c) secondary electron emission from the surface of the dust grains. [14] The co-existence of negatively and positively charged dust grains has been investigated in space [12,14] and laboratory pl...

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