The coupled Boussinesq-Burgers system is a physical model of fluid flows in a dynamical system that describes the propagation of shallow water waves. In this work, we upgrade this model to include time-fractional derivatives. The effect of the fractional order in the propagation of the obtained solutions is discussed by using an adaptation of both the time-spectrum function method and the homotopy perturbation method. One of the main findings worth to be mentioned, is that the field functions involved in the coupled fractional Boussinesq-Burgers system have different stability behaviors. Tables and 3D plots regarding the accuracy of the proposed numerical methods are presented and comparison is made to show the preference of either method.
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