Fractional Calculus

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 RiemannLiouville 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 MittagLeffler and related functions.

Fractional Derivatives

FractionalD RiemannLiouville fractional derivative

CaputoD Caputo fractional derivative

NFractionalD numerical RiemannLiouville derivative

NCaputoD numerical Caputo derivative

Fractional Integral Transforms

LaplaceTransform Laplace transforms of fractional derivatives

InverseLaplaceTransform inverse Laplace transforms of fractional rational functions

Fractional Differential Equations

DSolve, DSolveValue solutions of fractional differential equations

AsymptoticDSolveValue asymptotic solutions of fractional differential equations

Fractional Special Functions

MittagLefflerE solution representations for fractional differential equations