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Fractional hyper-chaotic model with no equilibrium

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  • Mishra, Jyoti

Abstract

This paper considers a novel four dimensional dynamical model containing hyper-chaotic attractors. The concept fractional differential based on the exponential and Mittage–Leffler kernel were used to extend the classical version in order to include into the mathematical formulation the crossover in waiting time distribution. We have presented for both models the conditions under which the existence and the uniqueness of exact solutions are reached.We have used a newly established numerical scheme, that combines the fundamental theorem of fractional calculus and the Lagrange interpolation polynomial to solve the system numerically. We presented some numerical simulations for different values of fractional order, we compared both models with the existing one under the framework of fractional calculus. Our model has shown very new chaotic features in particular with the Atangana–Baleanu fractional derivative.

Suggested Citation

  • Mishra, Jyoti, 2018. "Fractional hyper-chaotic model with no equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 43-53.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:43-53
    DOI: 10.1016/j.chaos.2018.09.009
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    References listed on IDEAS

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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    3. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
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    Cited by:

    1. Mishra, Jyoti, 2019. "Modified Chua chaotic attractor with differential operators with non-singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 64-72.

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