NCaputoD

NCaputoD[f, {x, α}, x0] gives a numerical approximation to the Caputo fractional derivative C₀Dₓᵅf(x) of order α of the function f at the point x0.

Examples

Fractional derivative of sine:

NCaputoD[Sin[x], {x, 0.5}, 1.0]

Half derivative of polynomial:

NCaputoD[x^2, {x, 0.5}, 2]

Compare different orders:

Table[NCaputoD[Exp[x], {x, a}, 1], {a, 0.1, 0.9, 0.2}]

Please visit the official Wolfram Language Reference for more details.