This paper proposes a hybrid controller that combines conventional proportional-resonant controllers with the more recent application of fractional order calculus applied to the current control loop of voltage source converters. The use of existing non-integer orders applied to proportional-integral controllers is extended to resonant controllers. The application of fractional exponents for the integro-derivative parts contributes with an extra degree of freedom that permits to enhance the obtained response in an extended frequency range when the closed-loop bode diagram is analysed. Different implementation alternatives in the continuous time domain are presented, and the most suitable one is selected. The new controller formulation capabilities are compared with conventional proportional-resonant controllers via simulations and its performance is validated in a test platform based on a 20 kVA silicon-carbide converter acting as an active filter.