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Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative

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Abstract.

In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.

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Authors and Affiliations

  1. International College, Hunan University of Arts and Science, 415000, Changde, China

    Shaobo He, Xiaoyong Mei, Bo Yan & Siwei Xu

  2. School of Physics and Electronics, Central South University, 410083, Changsha, China

    Kehui Sun

Authors
  1. Shaobo He
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  2. Kehui Sun
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  3. Xiaoyong Mei
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  4. Bo Yan
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  5. Siwei Xu
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Correspondence to Shaobo He.

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He, S., Sun, K., Mei, X. et al. Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative. Eur. Phys. J. Plus 132, 36 (2017). https://doi.org/10.1140/epjp/i2017-11306-3

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  • DOI: https://doi.org/10.1140/epjp/i2017-11306-3

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