PredictorCorrector-FracDiffEq

MATLAB implementation of a Predictor-Corrector Scheme for Solving Nonlinear Delay Differential Equations of Fractional Order

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" 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 file for details.