Comparison with other toolboxes

There are also some toolboxes that can be used for fractional differential equations, here we make a survey of all these toolboxes and have a more intuitive perspective.

FOTF toolbox is a Matlab toolbox developed by Prof Dingyu Xue, with fractional calculus, fractional differential equations and fractional order systems integrated together. To be honest, FOTF has a great impact on FractionalDiffEq.jl, all of the algorithms in FOTF toolbox is all supported in FractionalDiffEq.jl

corresponding APIs:

FOTF toolbox	FractionalDiffEq.jl
`fode_sol9`	`ClosedForm`
`fode_solm`	`ClosedFormHankelM`
`nlfode_vec`	`NonLinearAlg`

Matrix approach to discretization of ODEs and PDEs of arbitrary real order

The corresponding matrix discretization paper and toolbox is developed by Prof Igor Podlubny. The corresponding matrix discretization method in FractionalDiffEq.jl is FODEMatrixDiscrete and FPDEMatrixDiscrete.

FLMM2 Toolbox

FLMM2 toolbox is a toolbox developed by Prof Roberto Garrappa together with his paper

Exsiting	FractionalDiffEq.jl
`FLMM2(method=1)`	`Trap`
`FLMM2(method=2)`	`NewtonGregory`
`FLMM2(method=3)`	`BDF`
`fde12`	`PECE`
`mt_fde_pi1_ex`	`MTPIEX`
`mt_fde_pi1_im`	`mTPIRect`
`mt_fde_pi2_im`	`MTPITrap`
`mt_fde_pi12_pc`	`MTPECE`

Python

fodeint: With explicit one-step Adams-Bashforth (Euler) method.

R

Don't see any packages for fractional differential equations.