Fractional calculus generalizes the operations of differentiation and integration by unifying them into a single fractional derivative of arbitrary order. Fractional calculus is used in finance, engineering, science and other fields. The Wolfram Language provides tools for computing fractional derivatives using the Riemann–Liouville and Caputo definitions, as well as for using the popular Laplace transform technique to solve systems of linear fractional differential equations with constant coefficients in terms of the Mittag–Leffler and related functions.
FractionalD — Riemann–Liouville fractional derivative
CaputoD — Caputo fractional derivative
LaplaceTransform — Laplace transforms of fractional derivatives
InverseLaplaceTransform — inverse Laplace transforms of fractional rational functions
DSolve — solutions of fractional differential equations
MittagLefflerE — solution representations for fractional differential equations