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One of the most important steps in recognizing fingerprint is accurate feature extraction of the input image. To enhance the accuracy of fingerprint recognition, an algorithm using fractional derivatives is proposed in this paper. The proposed algorithm uses the definitions of fractional derivatives Riemann-Liouville (R-L) and Grunwald-Letnikov (G-L) in two sections of direction estimation and image enhancement for the first time. Based on it, new mask of fractional derivative Gabor filter is calculated. The proposed fractional derivative-based method enhances the image quality. This method enhances the structure of ridges and grooves of fingerprint, using fractional derivatives. The efficiency of the proposed method is studied in images of FVC2004 (DB1, DB2, DB3 and DB4) database and the results are evaluated using the criteria including entropy, average gradient, and edge intensity. Also, performance of the proposed method is compared with other technical methods such as Gabor filter. Based on the obtained results from the tests, the method is able to enhance the quality of fingerprint images significantly.