Comparison with other tools

Here we compare the current tools can be used to computing fractional calculus with FractionalCalculus.jl.


While most packages are encoded in Matlab, we would elaborate more on this section

Matrix Discretization

The Matrix Discretization method is a Matlab toolbox developed by Professor Igor Podlubny. FractionalCalculus.jl also support this method, the relating API is RLDiff_Matrix and RLInt_Matrix.


FOTF is a Matlab toolbox developed by Professor Dingyu Xue, it can be used to modeling and analysis fractional order systems. FOTF contains various methods to compute fractional calculus, FractionalCalculus.jl adapted all the methods in this toolbox, the relating methods are:

GL_High_Precision and Caputo_High_Precision.


It is noteworthy that Chebfun also can be used to compute fractional calculus.

Detailed usage

There are only one algorithm in Chebfun regarding Riemann Liouville fractional derivative and integral.



fcpy is a Python package for computing fractional calculus built by SciFracX community. It is based on FractionalCalculus.jl


mpmath mpmath is a python library for arbitrary-precision floating-point arithmetic computing, it is noteworthy that mpmath also support fractional calculus computing.

The relating document is here: differint

Mpmath only support Riemann Liouville fractional derivative.


differint is a Python package for calculating fractional derivatives, the main algorithms are Riemann Liouville(RL), Grunwald Letnikov(GL) and improved Grunwald Letnikov(GLI) algorithms.


Didn't see any packages used to compute fractional calculus😟