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The Riemann-Liouville fractional derivative of a function $f(t)$ for a real $\alpha$ is:
$$ D^\alpha f(t) = \frac{d^{\lfloor \alpha \rfloor + 1}}{dt^{\lfloor \alpha \rfloor + 1}} \left( \frac{1}{\Gamma(1 - \text{frac}(\alpha))} \int_0^t \frac{f(\tau)}{(t-\tau)^{\text{frac}(\alpha)}} d\tau \right) $$
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