Volume 3, Issue 1, May 2013, Pages 105–111
A. A. M. Arafa1, S. Z. Rida2, and H. M. Ali3
1 Department of mathematics, Faculty of Science, Port Said University, Port Said, Egypt
2 Department of mathematics, Faculty of Science, South Valley University, Qena, Egypt
3 Department of mathematics, Faculty of Science, Aswan University, Aswan, Egypt
Original language: English
Copyright © 2013 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, generalizations Mittag-Leffler function method is applied to solve approximate and analytical solutions of nonlinear fractional differential equation systems such as lorenz system of fractional oreder, and compared the results with the results of Homotopy perturbation method (HPM) and Variational iteration method (VIM) in the standard integer order form. The reason of using fractional order differential equations (FOD) is that fractional order differential equations are naturally related to systems with memory which exists in most systems. Also they are closely related to fractals which are abundant in systems. The results derived of the fractional system are of a more general nature. Respectively, solutions of fractional order differential equations spread at a faster rate than the classical differential equations, and may exhibit asymmetry. A few numerical methods for fractional differential equations models have been presented in the literature. However many of these methods are used for very specific types of differential equations, often just linear equations or even smaller classes put the results generalizations Mittag-Leffler function method show the high accuracy and efficiency of the approach. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense.
Author Keywords: Lorenz system, Caputo fractional derivative, Mittag-Leffler function, Variational iteration method, Fractional differential equation systems.
A. A. M. Arafa1, S. Z. Rida2, and H. M. Ali3
1 Department of mathematics, Faculty of Science, Port Said University, Port Said, Egypt
2 Department of mathematics, Faculty of Science, South Valley University, Qena, Egypt
3 Department of mathematics, Faculty of Science, Aswan University, Aswan, Egypt
Original language: English
Copyright © 2013 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, generalizations Mittag-Leffler function method is applied to solve approximate and analytical solutions of nonlinear fractional differential equation systems such as lorenz system of fractional oreder, and compared the results with the results of Homotopy perturbation method (HPM) and Variational iteration method (VIM) in the standard integer order form. The reason of using fractional order differential equations (FOD) is that fractional order differential equations are naturally related to systems with memory which exists in most systems. Also they are closely related to fractals which are abundant in systems. The results derived of the fractional system are of a more general nature. Respectively, solutions of fractional order differential equations spread at a faster rate than the classical differential equations, and may exhibit asymmetry. A few numerical methods for fractional differential equations models have been presented in the literature. However many of these methods are used for very specific types of differential equations, often just linear equations or even smaller classes put the results generalizations Mittag-Leffler function method show the high accuracy and efficiency of the approach. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense.
Author Keywords: Lorenz system, Caputo fractional derivative, Mittag-Leffler function, Variational iteration method, Fractional differential equation systems.
How to Cite this Article
A. A. M. Arafa, S. Z. Rida, and H. M. Ali, “Generalized Mittag-Leffler function method for solving Lorenz system,” International Journal of Innovation and Applied Studies, vol. 3, no. 1, pp. 105–111, May 2013.
