Numerical error too high

[AndresCenteno]

I'm doing the most simple Caputo derivative
$$^C_0 D_t^\alpha t = \frac{t^{1-\alpha}}{\Gamma(2-\alpha)}$$
and I get a relative error of $0.024$ for a time step of $10^{-9}$, is this supposed to be working properly?

using FractionalCalculus
using SpecialFunctions: gamma

T = 0.6; α = 0.9; Δt = 1e-9
numerical_caputo_der = fracdiff(t->t,α,0,T,Δt,CaputoDirect())[1]
theoretical_caputo_der = T^(1-α)/gamma(2-α)
abs(numerical_caputo_der-theoretical_caputo_der)/abs(theoretical_caputo_der) # 0.0239

[ErikQQY]

What is the version of package you are using for the computing? I just tested on master branch:
Numerical:

julia> numerical_caputo_der = fracdiff(t->t,α,T,0.001,CaputoDiethelm())
0.9987906107845391

Analytical:

theoretical_caputo_der = T^(1-α)/gamma(2-α)
0.9987906107845398

Error:

julia> abs(numerical_caputo_der-theoretical_caputo_der)/abs(theoretical_caputo_der)
6.669404053086289e-16

[ErikQQY]

Also, using such a small step size is bad

[AndresCenteno]

FractionalCalculus v0.2.10
I tried with a bunch of stepsizes! But the CaputoDiethelm works for me, so... it's ok now
I saw in the docs that you use CaputoTrap() for example, but it throws me an error saying it is not defined

[ErikQQY]

Just tagged a new major release, which should fix the "not defined" errors