FdeSolver
FdeSolver.jl: A Julia package for the numerical solution of fractional differential equations (FDEs) as well as systems of equations.
Science Score: 54.0%
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✓CITATION.cff file
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✓codemeta.json file
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○.zenodo.json file
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✓DOI references
Found 24 DOI reference(s) in README -
✓Academic publication links
Links to: mdpi.com, zenodo.org -
○Committers with academic emails
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○Scientific vocabulary similarity
Low similarity (13.3%) to scientific vocabulary
Keywords
Repository
FdeSolver.jl: A Julia package for the numerical solution of fractional differential equations (FDEs) as well as systems of equations.
Basic Info
- Host: GitHub
- Owner: JuliaTurkuDataScience
- License: other
- Language: Julia
- Default Branch: main
- Homepage: https://juliaturkudatascience.github.io/FdeSolver.jl/stable/readme/
- Size: 13.4 MB
Statistics
- Stars: 17
- Watchers: 1
- Forks: 4
- Open Issues: 2
- Releases: 11
Topics
Metadata Files
README.md
FdeSolver.jl: Solving fractional differential equations
This is a Julia package for fractional differential equations and ODEs. It provides numerical solutions for nonlinear fractional ordinary differential equations (in the sense of Caputo).
Related work includes the independent FractionalDiffEq Julia Package that provides solutions of differential equations with different fractional operators, and earlier tools that are available in Matlab.
The implemented models are generic and broadly applicable to modeling multivariate signals from a single source or collected across multiple sources. The dynamical models implemented in this package were initially developed for modeling dynamics of interacting microbial communities (Khalighi et al. 2022) but the models are more broadly applicable and applicable to studying multi-omic and host-microbiome interactions.
Method
We implement the predictor-corrector algorithms with a sufficient convergence and accuracy, including fast Fourier transform technique that gives us high computation speed. Interested readers can also find the stability of the methods and see how to implement the methods for solving multi-term fractional differential equations.
Let us suppose the following initial value problem with the Caputo fractional derivative for $\beta>0$:
math
{}_{C}\!D_{t_0}^{\beta}y(t)=f(t,y(t))
with the initial condition:
math
y(t_0)=y_0,y^{(1)}(t_0)=y^{(1)}_0,...,y^{(m-1)}(t_0)=y^{(m-1)}_0
where m is the smallest integer or equal to the order of derivative.
We solve the problem by using predictor corrector and Newton Raphson method.
Installation
If Julia is installed correctly, you can import FdeSolver.jl as:
julia
import Pkg; Pkg.add("FdeSolver")
A few methods on its usage are explained in Examples.
Acknowledgments
We are grateful to all contributors. New issues and pull requests are welcome.
This research has received funding from * the Horizon 2020 Programme of the European Union within the FindingPheno project under grant agreement No 952914. * Research Council of Finland (grant 330887)
Package documentation is compiled according to the guidelines provided in PkgTutorial.jl.
Publications
Kindly cite this work as follows:
- Fdesolver: A Julia package for solving fractional differential equations. M Khalighi, G Benedetti, L Lahti. ACM Transactions on Mathematical Software, 2024, doi.org/10.1145/3680280.
The package development is further linked with the following publications/preprints:
Ebola epidemic model with dynamic population and memory, F Ndaïrou, M Khalighi, and L Lahti, Chaos, Solitons & Fractals, 170: 113361, 2023, doi:10.1016/j.chaos.2023.113361.
Quantifying the impact of ecological memory on the dynamics of interacting communities. M Khalighi, G Sommeria-Klein, D Gonze, K Faust, L Lahti. PLoS Computational Biology 18(6), 2022, doi:10.1371/journal.pcbi.1009396.
Three-species Lotka-Volterra model with respect to Caputo and Caputo-Fabrizio fractional operators. M Khalighi, L Eftekhari, S Hosseinpour, L Lahti. Symmetry 13 (3):368, 2021, doi:10.3390/sym13030368.
Owner
- Name: JuliaTurkuDataScience
- Login: JuliaTurkuDataScience
- Kind: organization
- Repositories: 3
- Profile: https://github.com/JuliaTurkuDataScience
Citation (CITATION.bib)
@software{Benedetti:2022,
author = {Giulio Benedetti, Moein Khalighi, Leo Lahti},
title = {FdeSolver.jl: Solving fractional differential equations},
year = 2022,
publisher = {Zenodo},
doi = {10.5281/zenodo.5906104},
url = {https://doi.org/10.5281/zenodo.5906104}
}
GitHub Events
Total
- Watch event: 1
- Delete event: 3
- Push event: 2
Last Year
- Watch event: 1
- Delete event: 3
- Push event: 2
Committers
Last synced: almost 3 years ago
All Time
- Total Commits: 267
- Total Committers: 7
- Avg Commits per committer: 38.143
- Development Distribution Score (DDS): 0.581
Top Committers
| Name | Commits | |
|---|---|---|
| Giulio Benedetti | g****0@g****m | 112 |
| RiboRings | 8****s@u****m | 70 |
| Moein Khalighi | 5****8@u****m | 59 |
| MoeinKhalighi | m****i@g****m | 18 |
| moeinkh88 | m****i@g****m | 5 |
| CompatHelper Julia | c****y@j****g | 2 |
| antagomir | l****i@i****i | 1 |
Committer Domains (Top 20 + Academic)
Issues and Pull Requests
Last synced: 6 months ago
All Time
- Total issues: 1
- Total pull requests: 7
- Average time to close issues: over 3 years
- Average time to close pull requests: 9 days
- Total issue authors: 1
- Total pull request authors: 4
- Average comments per issue: 3.0
- Average comments per pull request: 0.57
- Merged pull requests: 6
- Bot issues: 0
- Bot pull requests: 1
Past Year
- Issues: 0
- Pull requests: 1
- Average time to close issues: N/A
- Average time to close pull requests: 7 minutes
- Issue authors: 0
- Pull request authors: 1
- Average comments per issue: 0
- Average comments per pull request: 0.0
- Merged pull requests: 1
- Bot issues: 0
- Bot pull requests: 0
Top Authors
Issue Authors
- moeinkh88 (1)
- antagomir (1)
Pull Request Authors
- RiboRings (4)
- moeinkh88 (2)
- antagomir (2)
- github-actions[bot] (1)
Top Labels
Issue Labels
Pull Request Labels
Packages
- Total packages: 1
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Total downloads:
- julia 2 total
- Total dependent packages: 1
- Total dependent repositories: 0
- Total versions: 12
juliahub.com: FdeSolver
FdeSolver.jl: A Julia package for the numerical solution of fractional differential equations (FDEs) as well as systems of equations.
- Homepage: https://juliaturkudatascience.github.io/FdeSolver.jl/stable/readme/
- Documentation: https://docs.juliahub.com/General/FdeSolver/stable/
- License: MIT
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Latest release: 1.0.9
published over 1 year ago