A new approach to controlling quadcopter unmanned aerial vehicles (UAVs) incorporating fractional calculus and a new prescribed performance function (PPF) in the design of a nonsingular terminal synergetic control (NSTSC) to control the quadcopter's attitude dynamics. Employing fractional calculus enables the establishment of a flexible control design that improves tracking accuracy, minimizes chattering, and enhances the robustness of the controller. Moreover, the new PPF is a simple function employed to improve the transient response and guarantee the controller's convergence within a finite time while simultaneously allowing the overshoot due to the rapid change in the quad-copter thrust directions. The objective of the study is to evaluate the efficiency of the proposed controller in tracking the desired orientation with accuracy while ensuring finite time convergence of the error. Furthermore, the Lyapunov technique is employed to demonstrate the stability of the closed-loop systems. The experimental results show that the use of finite time fractional nonsingular terminal synergetic control (FTFNTSC) leads to superior performance in tracking the quadcopter's orientation trajectories and more effective handling of system variations and external disturbances with a fast transient response, making it more promising approach for the morphing quadcopter system compared to the traditional synergetic control approach.