The concept of fractional-order control (F-oC) is exploited in this paper to synchronize fractional-order dynamical systems. The addressed systems in this paper reflect the real physical phenomena characterized by the complicated relationship between supply and demand for energy resources in the Shanghai area. Thus, we provide the developed fractional energy resource attractor and the simulation results regarding synchronization under the proposed control law of the same fractional energy resource attractor. Note that most of the synchronization methods achieved excellent performance when dealing with complex continuous systems; however, no method addressed the synchronization problem of fractional-order energy resource systems based on the F-oC and modern optimization techniques, to the best of our knowledge. By designing the finite-time control theory, the finite-time full synchronization of two identical fractional-order energy resources demand-supply hyperchaotic systems (F-oERDSHSs) is investigated due to its performance. The advanced prediction-based fractional-order control law (Pb-FoCL) is established for finite-time synchronization of F-oERDSHSs. The design procedure becomes a multiobjective optimization problem of the knowledge base of the developed controller while satisfying the desired performance requirements. The Finite-Time Stability (F-TS) of the control-loop system is proved by using the finite-time Lyapunov stability theory. Furthermore, the Improved Artificial Hummingbird Algorithm (I-AHA) is used to find an optimal knowledge base of Pb-FoCL while achieving the design constraints. Simulation results are provided to verify the efficiency of the proposed control strategy.