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The present paper deals with the theoretical investigation of the combined influence of Coriolis force, electrical resistivity, electron plasma frequency and fine dust particles on the linear Jeans instability of gaseous plasma by using the generalized magneto-hydrodynamic fluid model. The general dispersion relation is derived using normal mode analysis technique and reduced for both the longitudinal and transverse mode of propagation and further, it is discussed of the axis of rotation parallel and perpendicular to the magnetic field. We found that the stabilizing influence of Coriolis force and electron plasma frequency increases for a fine dust particle, but electrical resistivity has the destabilizing influence on them. The Jeans criterion of instability is modified by fine dust particle only transverse mode of propagation when rotation is perpendicular to the magnetic field. The Coriolis force and electron plasma frequency have stabilized the growth rate of the system but the electrical resistivity is destabilizing the system. These results are applicable to interstellar clouds and star formation region.
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