A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

► An algorithm onto discretize the analytical approximate solution of FOS is given.
► Definitions and operations of Fractional Differential Transformation Method (FDTM).
► A multi-step FDTM is proposed.
► The method does not require phase space reconstruction of fractional systems.
► Numerical validations on the fractional order Lorenz and Rossler systems.