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2. Definitions of half-finish
2.1 Riemann-Liouville half-derivative
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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