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Irving–Mullineux oscillator via fractional derivatives with Mittag-Leffler kernel

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  • Gómez-Aguilar, J.F.

Abstract

Recently, Abdon Atangana and Dumitru Baleanu suggested a novel fractional operator based in the Mittag-Leffler function with non-singular and nonlocal kernel. In this paper using the newly established fractional operator, an alternative representation of the Irving–Mullineux oscillator via Atangana–Baleanu fractional derivative in Liouville–Caputo sense is presented. Numerical simulations are obtained using an iterative scheme via Sumudu-Picard iterative method. The existence and uniqueness of the solutions are studied in detail using the fixed-point theorem and some properties of the inner product and the Hilbert space. Numerical simulations of the special solutions were done and new chaotic behaviors are obtained.

Suggested Citation

  • Gómez-Aguilar, J.F., 2017. "Irving–Mullineux oscillator via fractional derivatives with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 179-186.
    • Handle: RePEc:eee:chsofr:v:95:y:2017:i:c:p:179-186
    DOI: 10.1016/j.chaos.2016.12.025
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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 & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Reyes-Reyes, J. & Adam-Medina, M., 2016. "Modeling diffusive transport with a fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 467-481.
    4. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.
    5. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
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    Cited by:

    1. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.

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