Pullback D−attractors for the fractional non-autonomous beam equation with fractional rotational inertia and structural damping or strong damping

This paper investigates the well-posedness and long-time dynamics of a class of fractional non-autonomous beam equations with fractional rotational inertia and structural damping or strong damping. We prove that if $1\le p<p^{{\theta }_2}\equiv \frac{N+4{\theta }_2}{{(N-4{\theta }_2)}^{+}}$ $(\frac{1}{2}\le {\theta }_2\le 1)$, then: (i) The initial–boundary value problem (IBVP) of the equations admits a unique solution in $X_{{\theta }_2}^{{\theta }_1}$; (ii) there exists a pullback $D-$attractor for the non-autonomous dynamical system $(\varphi ,\theta )$. We provide a systematic proof of pullback $D-$attractors and extend the existing results on non-autonomous beam models. The findings establish a theoretical foundation for future practical applications.