In this article, we study a Caputo fractional model, namely, the time fractional damped Burger equation. As the main mathematical tool of this article, we apply a new approximate method which is called the approximate-analytical method (AAM) to deal with the time fractional damped Burger equation. Then, a new approximate solution of this considered equation was obtained. It may be used to characterize nonlinear phenomena of the shallow water wave phenomena. Thereby, it provides a new window for us to find the time fractional damped Burger equation new evolutionary mechanism.
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