RiemannLiouvilleFractionalDerivative - crowlogic/arb4j GitHub Wiki

The Riemann-Liouville fractional derivative of a function $f(t)$ for a real $\alpha$ is:

$$ D^\alpha f(t) = \frac{d^{\lfloor \alpha \rfloor + 1}}{dt^{\lfloor \alpha \rfloor + 1}} \left( \frac{1}{\Gamma(1 - \text{frac}(\alpha))} \int_0^t \frac{f(\tau)}{(t-\tau)^{\text{frac}(\alpha)}} d\tau \right) $$