Decay of solutions toa water wave model with a nonlocal viscous dispersive term

In this article, we investigate a water wave model with a nonlocal viscous term $ u_t+u_x+\beta $u_xxx$+\frac{\sqrt{\nu}}{\sqrt{\pi}}\int_0^t \frac{u_t(s)}{\sqrt{t-s}}ds+$uu_x$=\nu $u_xx$. $ The wellposedness of the equation and the decay rate of solutions are investigated theoretically and numerically.