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In this paper, the homotopy analysis method (HAM) is applied to the time fractional Whitham-Broer-Kaup equation to obtain its approximate analytical solutions. The HAM solution includes an auxiliary parameter ~ which provides a suitable way of adjusting and controlling the convergence region of solution series. AMS Subject Classification: 35A25, 58B05

APPROXIMATE ANALYTICAL SOLUTION OF THE TIME FRACTIONAL WHITHAM-BROER-KAUP EQUATION USING THE HOMOTOPY ANALYSIS METHOD