One-dimensional fluid simulations are used to study the dynamics of an electrostatic plasma sheath containing nanosized dust grains and two species of positive ions, i.e., He+ and Ar+. The impacts of the concentration of each species, the velocity at the sheath edge of the ions, and the bias voltage of the substrate, on the spatial distribution of the velocity and number density of the plasma particles, and the incident fluxes of the ions on the substrate, are investigated. The numerical results show that the sheath thickness increases with increasing σ, the density ratio of He+ ions to Ar+ ions at the sheath edge. For nanosized dust particles considered in this work, the dominant forces are the ion drag and the electric force and the effects of the neutral drag and gravity are negligible. Due to enhancement of the ion drag force and the electric force, the dust velocity increases and, consequently, the dust number density decreases as the concentration at the sheath edge of Ar+ ions is increased. For the same velocity and number density at the sheath edge, the number density of Ar+ ions near the wall is larger than that of He+ ions, but their incident fluxes are the same. The maximum in the dust number density increases with the velocity of Ar+ ions at the sheath edge, but it weakly changes with the Mach number of He+ ions, except for large values of σ. The position of the maximum dust number density initially decreases very quickly with increasing the velocity at the sheath edge of the ions from small values, but then at larger values it changes quite slowly. The differences in the sheath parameters for different values of σ disappear at some values of the velocity at the sheath edge of the ions and dust particles. The incident flux of the ions are independent of the bias voltage of the substrate, but their kinetic energy is equal to the bias potential.