Application of the Euler and Runge–Kutta Generalized Methods for FDE and Symbolic Packages in the Analysis of Some Fractional Attractors

  • 1 Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, Porto, Portugal
  • 2 Department of Mathematics, Polytechnic University of Timişoara, Timisoara, Romania
  • 3 Research Center in Theoretical Physics, West University of Timişoara, Timisoara, Romania
Constantin Milici, José Tenreiro MachadoORCID iD: https://orcid.org/0000-0003-4274-4879 and Gheorghe Drăgănescu

Abstract

This paper applies the Euler and the fourth-order Runge–Kutta methods in the analysis of fractional order dynamical systems. In order to illustrate the two techniques, the numerical algorithms are applied in the solution of several fractional attractors, namely the Lorenz, Duffing and Liu systems. The algorithms are implemented with the aid of Mathematica symbolic package. Furthermore, the Lyapunov exponent is obtained based on the Euler method and applied with the Lorenz fractional attractor.

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