Fractional Calculus and Shannon Wavelet

Abstract EN

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(ℝ) 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.