Pullback attractors of a strain gradient porous elastic system with fractional laplacian dissipations

In this research, we study a strain gradient porous elastic system with fractional dissipations of the Laplace operator. The model includes higher-order derivatives of the displacement in the basic postulates, which makes it more suitable than the classical theory of elasticity for studying essential questions related to size effects and nanotechnology. In the first instance, we prove the existence and uniqueness of both a generalized global solution and a strong solution, employing the semigroup theory of linear operators. Subsequently, we establish that the evolution process associated with the solutions of the non-autonomous problem admits a pullback attractor.