Polynomial stability for the Kawahara equation with internal fractional damping

The main concern of this article is to deal with the well-posedness, strong stability and polynomial stability of an initial-boundary-value problem related the Kawahara equation fifth-order, where we remove the nonlinear term and replace it with a dissipative term given by the fractional derivatives in the Caputo sense. The result obtained differs from all those discussed in the literature and has high application in various fields of science.