Due to the stochastic nature of EEG signals, various nonlinear patterns and methods have been applied in order to obtain characteristic understanding of their dynamic behavior [6]. The Fractal Dimension (FD) is an appropriate tool to analyzed EEG signals and can be calculated by means of the Higuchi's algorithm. Nevertheless, this algorithm depends of the k parameter to improve the speed of calculation. The aim of this work is to analyze the sensitivity of the k parameter due to segmentation, overlap, and noise over a signal. After that, with a better k parameter we applied the FD on EEG brain signals recorded while subjects were executing cognitive task. To analyze the statistical differences for each cognitive mental task, the hypothesis Wilcoxon signed-rank test was applied. The results for all tested brain bands used in this study reported a statistical difference (p < 0.05) in 9 out of 10 pairs of mental tasks. The proposed approach reported is a good tool for cognitive tasks discrimination. We have also determine better k parameter for different conditions therefore these results can be used for future studies.