We　consider　the　initial　value　problem　to　the　fractional　generalized　compressible　Navier-Stokes-Poisson　equations　for　viscous　fluids　with　one　Levy　diffusion　process　in　which　the　viscosity　term　appeared　in　the　fluid　equations　and　the　diffusion　term　for　the　internal　electrostatic　potential　are　described　respectively　by　the　nonlocal　fractional　Laplace　operators.　The　global-in-time　existence　of　the　smooth　solution　is　proven　under　the　assumption　that　the　initial　data　are　given　in　a　small　neighborhood　of　a　constant　state　in　the　sense　of　Sobolev＇s　space.　The　optimal　decay　rates　depending　upon　the　orders　of　two　fractional　Laplace　operators　are　established,　and　that　the　momentum　of　the　fractional　Navier-Stokes-Poisson　system　exhibits　a　slower　convergence　rate　in　time　to　the　constant　state　compared　to　that　of　the　fractional　compressible　Navier-Stokes　system　is　also　shown.　(c)　2025　Published　by　Elsevier　Inc.