Generalized Mittag-Leffler function method for solving Lorenz system

• Main Authors: Arafa, A.A.M., Rida, S.Z., Ali, H.M.
• Format: Article
• Language: English
• Published: Innovative Space of Scientific Research Journals 2013
• Subjects: QD Chemistry
• Online Access: http://eprints.um.edu.my/10570/1/Generalized_Mittag-Leffler_function_method_for_solving_Lorenz_system.pdf; http://eprints.um.edu.my/10570/
• Institution: Universiti Malaya

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.