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In this paper, a new approximate solution of time-fractional order multi-dimensional Navier–Stokes equation is obtained by adopting a semi-analytical scheme: “Fractional Reduced Differential Transformation Method (FRDTM)”. Three test problems are carried out in order to validate and illustrate the efficiency of the method. The scheme is found to be very reliable, effective and efficient powerful technique to solve wide range of problems arising in engineering and sciences. The small size of computation contrary to the other schemes, is its strength.