In this paper, we have studied a dusty plasma system including the nonthermal trapped electrons with Cairns– Gurevich distribution, mobile ions, and charge fluctuation stationary dust grains. Using the reduction perturbation technique, we have obtained two various differential equations governing this model of plasma. These equations are the modified nonlinear differential equations so-called the Schamel equation and the generalized Korteweg–de Vries (GKDV) equation. Analytical solutions show that the solitary waves can propagate in mentioned dusty plasma. Dispersion and nonlinear coefficients obtained depend on the trapping parameter (v), a nonthermal electron parameter (b), the ion-toelectron temperature ratio (ri) and the Maxwellian distribution (a). Also, the combined effect of an electron trapping and dust charge fluctuation on the nonlinear equation governing on this model was investigated. It is found that the amplitude and the width of solitary wave depend on trapped parameter, dust charge fluctuation, strength of non-Maxwellian distribution and nonthermal parameter. We have presented some physical explanations that support our results. The results of this study can be used to investigate the stability, instability of space, laser plasma interaction and laboratory plasma waves in which particles are trapped.
