Fractional Calculus and Shannon Wavelet

By Carlo Cattani. 2012

58 citations recorded by the source corpus.

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 <path id="x211D" d="M751 18q-1 -4 -2 -13t-2 -13q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -62 14 -77t74 -20v-28h-382v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h372q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172 q27 -52 89 -144q49 -71 81 -104q31 -36 72 -47zM543 469q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247h48q73 0 108 29q55 42 55 124zM290 131v390q0 62 -7.5 79.5t-30.5 17.5q-24 0 -31.5 -17.5t-7.5 -79.5v-390q0 -62 7.5 -79.5t31.5 -17.5q23 0 30.5 17.5 t7.5 79.5z" /> 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.

Subfields: Applied Mathematics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/b3e94ed011c978462f3463e53c7a27875829909b

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In Applied Mathematics

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

On Fractional Order Hybrid Differential Equations (2014, methodology): “[15] discussed a generalization of (2) by replacing the classical differentiation by fractional derivative in the Riemann-Liouvile sense as d α”