In this paper, four different algorithms present a comparative study of edge detection algorithms based on different fractional order differentiation. The first two algorithms present different fractional masks for the edge detection. Then, the other two algorithms use genetic algorithm to get better edge detection using the previous fractional masks. A fully automatic way to get the number of thresholds for each image using K-means principle is used. The performance comparison is done between different fractional algorithms with and without genetic algorithm. The performance comparison upon the addition of salt and pepper noise is evaluated by measuring the peak signal to noise ratio (PSNR) and bit error rate (BER). From results, it can be concluded that fractional edge detection based on genetic algorithm enhances performance.