Fractional calculus and Shannon wavelet. (English) Zbl 1264.42016

Summary: 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 \(L_2(\mathbb R)\) 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.


42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
94A17 Measures of information, entropy
26A33 Fractional derivatives and integrals
65T60 Numerical methods for wavelets
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