Cardiac ailments are increasing at an alarming rate globally due to the sedentary lifestyle and increased desk-bound activities. For decades, the ECG signal is used in aiding the analysis of human heart. Arrhythmia is a disorder that alters the normal cardiac cycle of ECG signal. The automatic classification of arrhythmia is a highly desirable and tough task. Mainly, the traditional methods of arrhythmia classification, are evaluated on the intra-patient criterion that may not befit the inter-patient criterion. A complete classification method has been proposed in the paper which performs well in intra-patient, inter-patient criterion and it is effective for minority class of MIT-BIH arrhythmia database (MIT-BIH-AD). In the proposed method, after preliminary processing based on Riesz fractional-order digital differentiator and R-peak detection, various features are extracted from ECG beat. The feature set proposed is a fusion of time-domain, time–frequency domain features and the new and novel features based on the Fibonacci series and coefficients of fractional-order Riesz based derivative signals which are proposed in this work. The results are evaluated on the MIT-BIH-AD and the results for intra-patients’ criterion have achieved an overall accuracy, sensitivity and positive predictivity values of 99.85%, 99.16%, 99.93% respectively, and for the inter-patient scheme 92.5%, 89.89% and 95.54% an average value of accuracy, sensitivity and positive predictivity of six ECG classes. The obtained results in both criterions have outperformed other methods in the literature and the proposed work has also attained better results for minority class of MIT-BIH-AD in both the scheme.