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Theory and application for the system of fractional Burger equations with Mittag leffler kernel

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  • Korpinar, Zeliha
  • Inc, Mustafa
  • Bayram, Mustafa

Abstract

In this work, the system of fractional Burger differential equations are presented as a new fractional model for Atangana–Baleanu fractional derivative with Mittag leffler kernel. The approximate consequences are analysed by applying an recurrent process. The existence and uniquenes of solution for this system is discussed. In order to appear the effects of several parameter and variables on the movement, the approximate results are showed in graphics and are compared with obtained solutions for two different derivative in tables.

Suggested Citation

  • Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307738
    DOI: 10.1016/j.amc.2019.124781
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    References listed on IDEAS

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    1. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    2. Yang, Xiaojia & Ge, Yongbin & Zhang, Lin, 2019. "A class of high-order compact difference schemes for solving the Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 394-417.
    3. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
    4. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    5. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    6. 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.
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    Cited by:

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