Definitions of half-finish
Introduction to the fractional derivative

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Definitions of half-finish
Introduction to the fractional derivative

Authors : François DUBOIS, Ana Cristina GALUCIO, Nelly POINT

Publication date: April 10, 2010 | Lire en français

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2. Definitions of half-finish

2.1 Riemann-Liouville half-derivative

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2.1.1 Definition

We saw in the previous paragraph how to "half-integrate" a causal function of time. If we now derive this "half-integral", we obtain a "half-derivative", or a derivative of order one-half. This is what Riemann and Liouville proposed for a causal function u(•) at the end of the 19th century (see, for example, Volume 2 of the treatise by Courant and Hilbert

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