In the past decades research on Active Vibration Control (AVC) has found increasing interest in control of flexible thin-walled structures, mainly made of new advanced materials such as composite carbon fibre. These types of composite structures combine high stiffness with good flexibility in achieving complex shapes, and are mostly used in automotive and aerospace applications where they are often subjected to undesirable vibrations. In the field of AVC, a new type of sensor and actuator have become popular by using so-called smart materials, such as piezoelectric materials. Given their distributed nature, they can be easily mounted on different types of structures, thus making them smart structures. State-of-the-art controllers, such as Positive Position Feedback (PPF), are very sensitive to spillover effect due to uncontrolled vibration modes, and therefore they are found to be difficult to tune in the case of multi-mode control. Another important aspect regarding the controller is that, apart from being able to reduce structural vibrations, it should ensure robustness and closed-loop stability for the controlled system. In this sense, careful positioning of sensors and actuators can have a great influence. With the motivation of improving on the limitations of state-of-the-art controllers, in this thesis a novel AVC strategy based on fractional-order calculus is proposed, developed, and successfully applied in practice. First, a fractional-order Positive Position Feedback (PPF) compensator is proposed to overcome the limitations of the commonly used integer-order PPF such as: frequency spillover, amplitude amplification in quasi-static region of the closed-loop response, and difficult tuning in multi-mode control. Tuning parameters of the controller are obtained by optimizing both magnitude and phase response of the controlled plant. Results are shown by comparing performances of the standard integer-order PPF and the optimized fractional-order PPF, both on a simple 1-DOF plant and on measured frequency response data from a rectangular carbon fibre/epoxy composite plate with free edges. Secondly, a second version of the fractional-order PPF is proposed, and compared to the other controllers for the AVC of a rectangular carbon fibre/epoxy composite plate with free edges. The plate is excited orthogonally by a modal vibration exciter and controlled by Macro Fibre Composite (MFC) transducers. Vibration measurements are taken with a Laser Doppler Vibrometer (LDV) system. MFC actuator and sensor are positioned on the plate based on maximal modal strain criterion, in order to control the second natural mode of the plate. Both integer and fractional-order PPFs allow for the second mode to be effectively controlled, although the newly proposed fractional-order controllers are found to be more efficient in achieving the same performance with less actuation voltage, and more promising in reducing the spillover effect due to uncontrolled modes.