Asymptotic analysis of the biharmonic Schrödinger equation with fractional damping

In this paper, we study the decay behavior of solutions to the biharmonic Schrödinger equation under the effect of internal fractional damping. By employing semigroup theory and energy methods, we establish well-posedness results and investigate the long-time behavior of solutions. In particular, we prove polynomial stability under suitable assumptions on the damping mechanism. Our results contribute to the understanding of how fractional damping influences the decay rate and stability of higher-order dispersive equations. These findings have potential applications in mathematical physics and control theory.