The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq-Whitham-Broer-Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann-Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann-Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.