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In this article, a hybrid technique called homotopy perturbation Elzaki transform method has been applied to solve Navier–Stokes equation of fractional order. In the hybrid technique, homotopy perturbation method and Elzaki transform method are amalgamated. Three example problems are solved with a purpose to validate and demonstrate the efficacy of the present method. It is also demonstrated that the results obtained from the present method are in excellent agreement with the results by other methods. It is shown that the proposed method is found to be reliable, efficient and easy to implement for various related problems of science and engineering.