一种求解分数阶非线性时滞微分方程的预测-校正算法的MATLAB实现.zip

# Fractional Order Differential Equations Solver This repository contains the unofficial MATLAB implementation of the algorithm presented in the paper ["A Predictor-Corrector Scheme For Solving Nonlinear Delay Differential Equations Of Fractional Order"](https://www.naturalspublishing.com/download.asp?ArtcID=1869) by Bhalekar and Daftardar-Gejji. The codebase is divided into three folders, corresponding to examples from Section 4 of the paper, titled "example1", "example2", and "example3". ## Description This implementation employs a predictor-corrector method for solving nonlinear delay differential equations of fractional order, as outlined in the referenced paper. Each example folder contains three MATLAB scripts: `main.m`, `fde_system.m`, and `plots.m`. - `fde_system.m`: Defines the fractional order differential equations system. - `main.m`: The main script for setting parameters and solving the equations. - `plots.m`: Visualizes the results. ## Structure - `example1/`: Code for Example 4.1 from the paper. - `example2/`: Code for Example 4.2. - `example3/`: Code for Example 4.3. Each folder includes: - `main.m`: Main executable script. - `fde_system.m`: Function defining the equations. - `plots.m`: Script for plotting results. ## Requirements - MATLAB version 2022a (likely compatible with other versions as the implementation doesn't rely on specific new features of MATLAB). ## Usage To run an example: 1. Navigate to the desired example folder (e.g., `example1`). 2. Run the `main.m` script in MATLAB. 3. The script will use `fde_system.m` for equation definitions and `plots.m` for visualizing results. ## Gallery Here is a visual comparison of some paper results and the results of my code:    ## Contributing Contributions, issues, and feature requests are welcome. Please check the issues page if you want to contribute. ## Reference The algorithm implemented in this repository is based on the following paper: > Bhalekar, S.; Daftardar-Gejji, V. A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order. J. Fract. Calc. Appl. 2011, 1, 1–9. ## License This project is licensed under the MIT License - see the [LICENSE](./LICENSE) file for details.