Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM

Authors

M. M. Khader, Department of Mathematics and Statistics, College of Science, Al-Imam Mohammed Ibn Saud Islamic University, Riyadh, Saudi Arabia and Department of Mathematics, Faculty of Science, Benha University, Benha, EgyptFollow
N. H. Sweilam
A. M. S. Mahdy

Author Country (or Countries)

Egypt

Abstract

This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense. The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton iteration method. The method introduces a promising tool for solving many systems of non-linear FDEs. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed methods. Comparisons with the fractional finite difference method (FDM) and the fourth order Runge-Kutta (RK4) are given.

Suggested Reviewers

N/A

Recommended Citation

M. Khader, M.; H. Sweilam, N.; and M. S. Mahdy, A. (2013) "Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM," Applied Mathematics & Information Sciences: Vol. 07: Iss. 5, Article 41.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss5/41