Symbolic fractional dynamics

• Author(s): Machado, J. A. Tenreiro ; Galhano, Alexandra
• Date: 2013
• Persistent ID: http://hdl.handle.net/10400.22/3759
• Origin: Repositório Científico do Instituto Politécnico do Porto
• Subject(s): Fractals; Fractional calculus; Multidimensional scaling; Scientific visualization; Symbolic dynamics
• Document Type: Article
• Language: English

Description

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.