Four-dimensional (4D) cone-beam CT (CBCT) reconstructs temporally-resolved phases of 3D volumes often with the same amount of projection data that are meant for reconstructing a single 3D volume. 4D CBCT is a sparse-data problem that is very challenging for high-quality 4D CBCT image reconstruction. Here we develop a new method, namely 4D-AirNet, that synergizes analytical and iterative method with deep learning for high-quality temporally-resolved CBCT slice reconstruction. 4D-AirNet is an unrolling method using the optimization framework of fused analytical and iterative reconstruction (AIR), which is based on proximal forward-backward splitting (PFBS). Three different strategies are developed for 4D-AirNet: random-phase (RP), prior-guided (PG), and all-phase (AP). RP-AirNet and PG-AirNet utilize phase-by-phase training and reconstruction, while PG-AirNet also uses a prior image reconstructed with all-phase projection data. Dense connectivity is built into 4D-AirNet networks for improved reconstruction quality. In contrast, AP-AirNet trains and reconstructs all phases simultaneously. In addition, the joint regularization method of DL and conventional spatiotemporal total variation (TV) is investigated. 4D-AirNet methods were evaluated in comparison with conventional iterative (TV) and deep learning (LEARN) methods, using simulated 2D-t CBCT scans from a lung dataset with various sparse-data levels. The reconstruction results suggest 4D-AirNet methods outperform TV and LEARN, and AP-AirNet provides the best reconstruction quality overall.