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
The Matrix Discretization method is a Matlab toolbox developed by Professor Igor Podlubny. FractionalCalculus.jl also support this method, the relating API is
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:
It is noteworthy that Chebfun also can be used to compute fractional calculus.
There are only one algorithm in Chebfun regarding Riemann Liouville fractional derivative and integral.
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😟