TY - JOUR A2 - Toma, Cristian AU - Cattani, Carlo PY - 2012 DA - 2012/08/07 TI - Fractional Calculus and Shannon Wavelet SP - 502812 VL - 2012 AB - 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 L2() 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. SN - 1024-123X UR - https://doi.org/10.1155/2012/502812 DO - 10.1155/2012/502812 JF - Mathematical Problems in Engineering PB - Hindawi Publishing Corporation KW - ER -