Abstract
This paper deals with the approximate and analytical solutions of non linear fractional differential equations namely, Lorenz System of Fractional Order and the obtained results are compared with the results of Homotopy Perturbation method and Variational Iteration method in the standard integer order form. The reason for using fractional order differential equations is that, fractional order differential equations are naturally related to systems with memory which exists in most systems and also they are closely related to fractals which are abundant in systems. The derived results are more general in nature. The solution of such equations spread at a faster rate than the classical differential equations and may exhibit asymmetry. A few numerical methods for the solution of fractional differential equation models have been discussed in the literature. However many of such methods are used for very specific types of differential equations, often just linear equations or even smaller classes, but this method shows the high accuracy and efficiency of the approach. Special cases involving the Mittag-Leffler function and exponential function are also considered. Keywords: Generalized Mittag-Leffler function, Caputo fractional derivative, Lorenz system. AMS 2010 Subject Classification: 26A33, 33E12.
Highlights
AND MATHEMATICAL PRELIMINARIESIt has been shown by that time fractional derivatives are equivalent to infinitesimal generators of generalized time fractional evolutions arising in the transition from microscopic to macroscopic time scales (Hilfer, 2002; 2003). Hilfer (2000) showed that this transition from ordinary time derivative to fractional time derivative arises in physical problems
This paper deals with the approximate and analytical solutions of non linear fractional differential equations namely, Lorenz System of Fractional Order and the obtained results are compared with the results of Homotopy Perturbation method and Variational Iteration method in the standard integer order form
The connection between the results obtained by solving fractional diffusion and fractional Fokker-Planck equations with those obtained from the continuous time random walk theory is another example of the importance of fractional derivatives (Metzler et al, 1999; Metzler and Klafter, 2000)
Summary
AND MATHEMATICAL PRELIMINARIESIt has been shown by that time fractional derivatives are equivalent to infinitesimal generators of generalized time fractional evolutions arising in the transition from microscopic to macroscopic time scales (Hilfer, 2002; 2003). Hilfer (2000) showed that this transition from ordinary time derivative to fractional time derivative arises in physical problems. A method for the solution of fractional differential equations using generalized Mittag-Leffler function
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