We applied detrended fluctuation analysis, power spectral density, and eigenanalysis of detrended cross-correlations to investigate fMRI data representing a diurnal variation of working memory in four visual tasks: two verbal and two nonverbal. We show that the degree of fractal scaling is regionally dependent on the engagement in cognitive tasks. A particularly apparent difference was found between memorisation in verbal and nonverbal tasks. Furthermore, the detrended cross-correlations between brain areas were predominantly indicative of differences between resting state and other tasks, between memorisation and retrieval, and between verbal and nonverbal tasks. The fractal and spectral analyses presented in our study are consistent with previous research related to visuospatial and verbal information processing, working memory (encoding and retrieval), and executive functions, but they were found to be more sensitive than Pearson correlations and showed the potential to obtain other subtler results. We conclude that regionally dependent cognitive task engagement can be distinguished based on the fractal characteristics of BOLD signals and their detrended cross-correlation structure.