  Dust-ion-acoustic (DIA) rogue waves (DIARWs) are investigated in a three
components dusty plasma system containing inertialess electrons featuring
non-thermal non-extensive distribution as well as inertial warm ions and
negative dust grains. A nonlinear Schr\"{o}dinger equation (NLSE), which
governs the conditions of the modulational instability (MI) of DIA waves
(DIAWs), is obtained by using the reductive perturbation method. It has been
observed from the numerical analysis of NLSE that the plasma system supports
both modulationally stable domain in which dispersive and nonlinear
coefficients of the NLSE have same sign and unstable domain in which dispersive
and nonlinear coefficients of the NLSE have opposite sign, and also supports
the DIARWs only in the unstable domain. It is also observed that the basic
features (viz. stability of the DIAWs, MI, growth rate, amplitude, and width of
the DIARWs, etc.) are significantly modified by the related plasma parameters
(viz. dust charge state, number density of electron and ion, non-extensive
parameter q, and non-thermal parameter $\alpha$, etc.). The present study is
useful for understanding the mechanism of the formation of DIARWs in the
laboratory and space environments where inertialess mixed distributed electrons
can exist with inertial ions and dust grains.
