In this paper 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 Grunwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.

Fractional calculus and Shannon Wavelet

CATTANI, Carlo
2012

Abstract

In this paper 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 Grunwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/3413077
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact