This study considers the terminal traffic flow problem and aims to minimize the total fuel consumed in extended terminal maneuvering areas (E-TMA) using a mixed-integer linear programming model. To reveal the benefits of the E-TMA concept, the exact solution solver is selected to determine optimal aircraft sequencing. Furthermore, the proposed model applies separation and sequencing maneuvers, including the point merge system (PMS), vector maneuvers (VM), and en route speed reduction maneuvers. An innovative mathematical model is presented for this problem. In this study, the proposed model is compared with two other approaches. The first uses VM and PMS without changing the initial sequencing. The second utilizes the VM and PMS maneuvers. Unlike the first approach, it searches for the optimum aircraft arrival sequencing. The results demonstrate that the proposed model could reduce total fuel consumption by 9.45% and 1.95% compared with the other two approaches.