Fractional calculus

Summary

Fractional calculus studies integrals and derivatives of non-integer order, such as a "half derivative". Its basic operator is the Riemann–Liouville integral, which extends repeated integration to any real order $\alpha > 0$. Fractional derivatives, such as the Riemann–Liouville, Caputo and Grünwald–Letnikov derivatives, are built from it or from limits of differences. These operators model memory effects and anomalous diffusion, and appear in integral equations such as Abel's equation.