This paper proposes modified modulation and control schemes for power decoupling of single-stage single-phase Cuk inverter in continuous conduction mode. Because it has inherent two inductors at the input and output side, the Cuk inverter is able to step up/down the voltage with reduced input and output current ripples. Thus, smaller filtering capacitance, especially at the input side, can be used which increases its suitability for photovoltaic applications. For the maximum power point tracking control, the oscillating even order harmonic components should be eliminated from the inverter’s input side otherwise the maximum power cannot be extracted. The proposed modulation scheme will ease the control of inverter’s input and output sides. Therefore, the 2nd order harmonic in the input current can be eliminated without adding new active semiconductor switches. In addition, the paper presents a control scheme using fractional-order repetitive control with a conventional proportional-resonant controller. With this closed-loop controller, a sinusoidal output grid current can be generated and controlled while the input current is kept constant with time