Solving System of Fractional Order Differential Equations Using Legendre Operational Matrix of Derivatives

Authors: Salisu Ibrahim1 & Abdulnasir Isah2
1Department of Mathematics Education, Faculty of education. Tishk International University, Erbil, Iraq
2Department of Mathematics Education, Faculty of education. Tishk International University, Erbil, Iraq

Abstract: This paper presents approximate solutions of linear system of fractional differential equations (FDEs) by extending the approach of shifted Legendre operational matrix of derivatives together with spectral method. The results obtained in solving differential systems of linear FDE shows that the proposed method is factual. Fractional differential equations (FDEs) have been a useful tool for computing and modelling of computer components in telecommunication companies, mobile companies and for industrial practitioners and also plays a vital role in science and engineering.

Download the PDF Document

doi: 10.23918/eajse.v7i1p25

References

Agarwal, R. P., Andrade, B., & Cuevas C. (2020). Weighted pseudo-almost periodic solutions of a class of semi linear fractional differential equations. Nonlinear Anal Real-World Appl. 11, 3532-3554 (2010). DOI: 10.1016/j.nonrwa .2010 .01.002

Agarwal, R. P., Lakshmikantham, V., & Nieto, J. J. (2010). On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. 72, 2859-2862. DOI:10.1016/j.na.2009.11.029

Diethelm, K., Ford, N. J., & Freed, A. D. (2002). A predictor-corrector approach for the numerical solution of fractional differential equation. Nonlinear Dyn. 29, 3-22.

Doha, E. H., Bhrawy, A. H., & Ezz-Eldien, S. S. (2011). A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput. Math. Appl. 62, 2364-2373.

Doha, E. H., Bhrawy, A. H., & Ezz-Eldien, S. S. (2012). A new Jacobi operational matrix: An application for solving fractional differential equations. Appl. Mathl. Modl. 36, 4931-4943.

Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and application of fractional differential equations, North Holland Mathematics studies, Vol. 204, Elsevier Science, Amsterdam.

Ibrahim, S. (2020). Numerical Approximation Method for Solving Differential Equations. Eurasian Journal of Science & Engineering, 6(2), 157-168.

Ibrahim, S., & Rababah, A. (2020). Degree Reduction of Bézier Curves with Chebyshev Weighted G^3-continuity. Advanced studies in Contemporary Mathematics, 4(30), 471 – 476.

Odibat, Z. (2011). On Legendre polynomial approximation with the VIM or HAM for numerical treatment of nonlinear fractional differential equations. J Comput. Appl. Math. 235, 2956-2968. doi: 10.1016/j.cam.2010.12.013.

Monami, S., & Odibat, Z. (2007). Numerical approach to differential equations of fractional. Compt. Appl. Math, 207(2007), 96-110.

Podlubny, I. (1999). Fractional Differential Equations, Mathematics in Science and Engineering. Academic Press Inc, San Diego, CA vol. 198.

Rababah, A., & Ibrahim, S. (2016a). Weighted G^1-Multi-Degree Reduction of Bézier Curves. International Journal of Advanced Computer Science and Applications, 7(2), 540-545. https://thesai.org/Publications/ViewPaper?Volume=7&Issue=2&Code=ijacsa&SerialNo=70

Rababah, A., & Ibrahim, S. (2016b). Weighted Degree Reduction of Bézier Curves with G^2-continuity. International Journal of Advanced and Applied Science, 3(3),13-18.

Rababah, A., & Ibrahim, S. (2018). Geometric Degree Reduction of Bézier curves, Springer Proceeding in Mathematics and Statistics, Book Chapter 8.https://www.springer.com/us/book/9789811320941

Ray, S. S., Chaudhuri, K. S., & Bere, R. K. (2006). Analytical approximate solution of nonlinear dynamic containing fractional derivative by modified decomposition method. Appl. Math. Comput. 182, 544-552.

Saadatmandi, A., & Dehghan, M. (2010). A new operational matrix for solving fractional-order differential equations. Comput. Math. Appl. 59, 1326-1336.

Samko, S. G., Kilbas, A. A., & Marichev, O. I. (1993). Fractional Integrals and Derivatives: Theory and Applications Gordon and Breach, Yverdon.

Yang, S., Xiao, A., & Su, H. (2010). Convergence of the variational iteration method for solving multi-order fractional differential equations. Comput. Math. Appl. 60, 2871-2879.