Pullback <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg" display="inline" id="d1e33"> <mml:mrow> <mml:mi mathvariant="script">D</mml:mi> <mml:mo>−</mml:mo> </mml:mrow> </mml:math> attractors for the fractional non-autonomous

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≤p<pθ2≡N+4θ2(N−4θ2)+ (12≤θ2≤1), then: (i) The initial–boundary value problem (IBVP) of the equations admits a unique solution in Xθ2θ1; (ii) there exists a pullback D−attractor for the non-autonomous dynamical system (ϕ,θ). 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.