This paper proposes and analyses the performance of a Genetic Algorithm (GA) using two new concepts, namely a static fitness function including a discontinuity measure and a fractional-order dynamic fitness function. The GA is adopted for the synthesis of combinational logic circuits. In both cases, experiments reveal superior results in terms of speed and convergence to achieve a solution. Categories and Subject Descriptors B.6.3 [Logic Design]: Design Aids – automatic synthesis, optimization. General Terms: Algorithms, Design.