Polynomial decay of porous elastic system with fractional damping

In this work, we prove that the effect of damping given by tempered Caputo derivative does not lead the porous elastic model to exponential stability. Although damping acts on both equations of the system, it is not strong enough to lead the model to exponential stabilization, which is novel for this type of model, where a single damping factor provides exponential stability depending on a relationship between the velocity coefficients. Thus, we prove that the model is well-posed and polynomially stable.