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The unified generalized non-local theory is applied for mathematical modeling of cosmic objects. For the case of galaxies the theory leads to the flat rotation curves known from observations. The transformation of Kepler’s regime into the flat rotation curves for different solitons is shown. The Hubble expansion with acceleration is explained as result of mathematical modeling based on the principles of non-local physics. Peculiar features of the rotational speeds of galaxies and effects of the Hubble expansion need not in the introduction of new essence like dark matter and dark energy. The origin of difficulties consists in the total Oversimplification following from the principles of local physics

To the Theory of Galaxies Rotation and the Hubble Expansion in the Frame of Non-Local Physics