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Numerical analysis of dissipative system with noise model with the Atangana–Baleanu fractional derivative

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  • Alkahtani, Badr Saad T.

Abstract

The model of dissipative system with noise has not been so far a center of interest of many researchers, while this model is very interesting physical problem that deserves to capture attentions. Not to mention that no study has been done for this model using the newly established concept of fractional differential operators based on non-singular kernels. In this paper, we aimed to provide an analysis mainly numerical analysis of the model with the non-local non-singular kernel differential operators. We made use of a recent powerful numerical scheme and provided some numerical simulations for different values of fractional order.

Suggested Citation

  • Alkahtani, Badr Saad T., 2018. "Numerical analysis of dissipative system with noise model with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 239-248.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:239-248
    DOI: 10.1016/j.chaos.2018.09.021
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. Algahtani, Obaid Jefain Julaighim, 2016. "Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 552-559.
    5. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    6. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
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