# 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.

## Matlab

### FOTF toolbox

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)` | `FLMMTrap` |

`FLMM2(method=2)` | `FLMMNewtonGregory` |

`FLMM2(method=3)` | `FLMMBDF` |

`fde12` | `ABM` |

`mt_fde_pi1_ex` | `PIEX` |

`mt_fde_pi1_im` | `PIIMRect` |

`mt_fde_pi2_im` | `PIIMTrap` |

`mt_fde_pi12_pc` | `PIPECE` |

## Python

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

## R

Don't see any packages for fractional differential equations.