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: and Gheorghe Drăgănescu


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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The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at researchers in nonlinear sciences, engineers, and computational scientists, economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.