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# FdeSolver: A Julia Package for Solving Fractional Differential Equations

This repository contains the benchmarking results between [FdeSolver.jl](https://github.com/JuliaTurkuDataScience/FdeSolver.jl), [FractionalDiffEq.jl](https://github.com/SciFracX/FractionalDiffEq.jl) and [MATLAB](https://www.dm.uniba.it/members/garrappa/software) solvers.

## How to navigate this repository

The benchmarking scripts are stored in the [_src_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/main/src/julia) directory and include the following cases:

* Single dimension
* Multiple dimensions
* Random parameters
* ...

To perform one or multiple benchmarks, use the [_run_benchmark.jl_](https://github.com/JuliaTurkuDataScience/2022_Khalighi_Benchmark/blob/merge_repos/run_benchmark.jl). Data files are generated and saved in the [_raw_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/main/data/raw) subdirectory of the [_data_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/main/data) directory.

Preprocessed data used to plot the figures are available in the [_data_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/main/data) directory, whereas raw data from the 6 benchmarks are found in the [_raw_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/main/data/raw) subdirectory.

Benchmarking plots can be generated by running the [_plot_benchmarking_results.jl_](https://github.com/JuliaTurkuDataScience/2022_Khalighi_Benchmark/blob/merge_repos/plot_benchmarking_results.jl) script and are saved in the [_results/benchmarking_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/merge_repos/results/benchmarking) subdirectory.

Microbial community simulation is performed by running the [_run_community_simulation.jl_](https://github.com/JuliaTurkuDataScience/2022_Khalighi_Benchmark/blob/merge_repos/run_community_simulation.jl) script and plots are saved in the [_results/community_simulation_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/merge_repos/results/community_simulation) subdirectory.

Covid-19 transmission fitting is performed by running the [_run_covid_fitting.jl_](https://github.com/JuliaTurkuDataScience/2022_Khalighi_Benchmark/blob/merge_repos/run_covid_fitting.jl) script and plots are saved in the [_results/covid_fitting_](https://github.com/JuliaTurkuDataScience/benchmarking_FDE_Matlab_SciFracx/tree/merge_repos/results/covid_fitting) subdirectoy.
