Fractional-order dierential equations are interesting for their applications in the construction of mathematical models in nance, materials science or diusion. In this paper, an application of a well known transformation technique, Dierential 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, frst introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dipendence 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.
A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems
CAPONETTO, Riccardo;
2013-01-01
Abstract
Fractional-order dierential equations are interesting for their applications in the construction of mathematical models in nance, materials science or diusion. In this paper, an application of a well known transformation technique, Dierential 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, frst introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dipendence 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.Pubblicazioni consigliate
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