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Mathematical Problems in Engineering
Volume 2012, Article ID 502812, 26 pages
Research Article

Fractional Calculus and Shannon Wavelet

Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 18 February 2012; Accepted 13 May 2012

Academic Editor: Cristian Toma

Copyright © 2012 Carlo Cattani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any function, reconstructed by Shannon wavelets, we can easily define its fractional derivative. The approximation error is explicitly computed, and the wavelet series is compared with Grünwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.