Comparison with other tools
Here we compare the current tools can be used to computing fractional calculus with FractionalCalculus.jl.
Matlab
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
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.
Chebfun
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.
Python
fcpy
fcpy is a Python package for computing fractional calculus built by SciFracX community. It is based on FractionalCalculus.jl
mpmath
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
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.
R
Didn't see any packages used to compute fractional calculus😟