The linear and non-linear dynamics of ion acoustic waves are investigated in three-component magnetized plasma consisting of cold inertial ions and non-thermal electrons and positrons. The non-thermal components are modelled by the hybrid distribution, representing the combination of two (kappa and Cairn's) non-thermal distributions. The relevant processes, including the slow rotation of plasma along the magnetic field axis and collision between ions and neutrals, are taken into consideration. It is shown that the non-linear dynamics of the considered system are governed by the Zakharov-Kuznetsov equation in modified form. In the general dissipation regime, the effects of the two non-thermal distributions on the solitary waves are compared. The effects of other plasma parameters, such as collisional and rotational frequency, are also discussed in detail. KEYWORDS Damped Zakharov-Kuznetsov Equation, Dissipative ion acoustic solitary waves, electron-positron-ion plasma 1