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Fractal Analysis is the well developed theory in the Non-linear Analysis of Biomedical Signals such as Electroencephalogram (EEG). EEG Biomedical signal is essentially multi scale fractal i.e., Multifractal. Therefore, quantifying the chaotic nature and complexity of the EEG Signal requires estimation of the Generalized Fractal Dimensions spectrum where the complexity means higher variability in general fractal dimension spectrum.We organize a novel technique for estimating the steepness of EEG signals from Epileptic Patients. The proposed idea is developed from the theory of ReÂ¿nyi Fractal Dimensions or Generalized Fractal Dimensions (GFD), which is based on the concept of generalized ReÂ¿nyi Entropy of a given probability distribution. The range of GFD shows the chaotic nature (irregularity) and complexity of the Biomedical Time Series. We estimate the steepness of EEG Fractal Time Series using the Steepness measure, which is defined from the GFD. We compare these measures for the EEG signals taken at different states and observe that there are significant differences between the values of Steepness measure for the Epileptic EEGs and Healthy EEGs. Finally we conclude that Epileptic EEGs has less complexity (less unexpected values) than the Healthy EEGs. These are the system of Multifractal techniques, which are very efficient tool in the Non-linear Analysis of Biomedical Signals to analyze, detect or predict the state of illness of the Epileptic patients.