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In this paper, two-hybrid techniques, namely q-homotopy analysis Elzaki transform method (q-HAETM) and iterative Elzaki transform method (IETM) have been applied to obtain the numerical solutions of time-fractional Navier-Stokes equations in polar coordinate described in the Caputo sense. q-HAETM is the combination of the homotopy analysis method and Elzaki transform method, and IETM is the combination of two reliable methods, i.e. iterative method and Elzaki transform method. Two example problems are solved, and the obtained results are compared with the solutions solved by other techniques which show the efficacy and powerfulness of the methods.

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