FractionalCalculus.jl
FractionalCalculus.jl provides support for fractional calculus computing.
π Installation
If you have already install Julia, you can install FractionalCalculus.jl in REPL using Julia package manager:
pkg> add FractionalCalculus
π¦Έ Quick start
Derivative
To compute the fractional derivative in a specific point, for example, compute
julia> fracdiff(x->x, 0.2, 1, 0.0001, RLDiffL1())
1.0736712740308347
This will return the estimated value with high precision.
Integral
To compute the fractional integral in a specific point, for example, compute the semi integral of
julia> fracint(x->x, 0.5, 1, 0.0001, RLIntApprox())
0.7522525439593486
This will return the estimated value with high precision.
π» All algorithms
Current Algorithms
βββ FracDiffAlg
β βββ Caputo
| | βββ CaputoDirect
| | βββ CaputoTrap
| | βββ CaputoDiethelm
| | βββ CaputoHighPrecision
| | βββ CaputoHighOrder
| |
β βββ GrΓΌnwald Letnikov
| | βββ GLDirect
| | βββ GLMultiplicativeAdditive
| | βββ GLLagrangeThreePointInterp
| | βββ GLHighPrecision
| |
| βββ Riemann Liouville
| | βββ RLDiffL1
| | βββ RLLinearSplineInterp
| | βββ RLDiffMatrix
| | βββ RLG1
| | βββ RLD
| |
| βββ Hadamard
| | βββ HadamardLRect
| | βββ HadamardRRect
| | βββ HadamardTrap
| |
| βββ Riesz
| | βββ RieszSymmetric
| | βββ RieszOrtigueira
| |
| βββ Caputo-Fabrizio
| | βββ CaputoFabrizioAS
| |
| βββ Atanagana Baleanu
| βββ AtanganaSeda
|
βββ FracIntAlg
βββ Riemann Liouville
| βββ RLDirect
| βββ RLPiecewise
| βββ RLLinearInterp
| βββ RLIntApprox
| βββ RLIntMatrix
| βββ RLIntSimpson
| βββ RLIntTrapezoidal
| βββ RLIntRectangular
| βββ RLIntCubicSplineInterp
|
βββ Hadamard
βββ HadamardMat
For detailed usage, please refer to our manual.
πΌοΈ Example
Let's see examples here:
Compute the semi-derivative of
We can see the computing retains high precision
Compute different order derivative of
Also different order derivative of
And also different order integral of
π§ Symbolic Fractional Differentiation and Integration
Thanks to SymbolicUtils.jl, FractionalCalculus.jl can do symbolic fractional differentiation and integration now!!
julia> using FractionalCalculus, SymbolicUtils
julia> @syms x
julia> semidiff(log(x))
log(4x) / sqrt(Οx)
julia> semiint(x^4)
0.45851597901024005(x^4.5)
π’ Status
Right now, FractionalCalculus.jl has only supports for little algorithms:
Fractional Derivative:
- Caputo fractional derivative
- Grunwald-Letnikov fractional derivative
- Riemann-Liouville fractional derivative
- Riesz fractional derivative
- Hadamard fractional derivative
- Caputo-Fabrizio fractional derivative
- Atangana-Baleanu fractional derivative
- Marchaud fractional derivative
- Weyl fractional derivative
- ......
Fractional Integral:
- Riemann-Liouville fractional integral
- Hadamard fractional integral
- Atangana-Baleanu fractional integral
- ......
π Reference
FractionalCalculus.jl is built upon the hard work of many scientific researchers, I sincerely appreciate what they have done to help the development of science and technology.
π₯ Contributing
If you are interested in Fractional Calculus and Julia, welcome to raise an issue or file a Pull Request!!