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Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative

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  • Inc, Mustafa
  • Yusuf, Abdullahi
  • Aliyu, Aliyu Isa
  • Baleanu, Dumitru

Abstract

This work presents analysis of the logarithmic-KdV equation involving new fractional operator called Atangana–Baleanu (AB) fractional derivative with Mittag-Leffler (ML) type kernel. The existence and uniqueness of the governing equation having AB fractional derivative with ML type kernel is proved with the aid of a fixed-point theorem. We present numerical simulations by using iterative algorithm. The effectiveness of various parameters and variables on the displacement are presented in Figures 1 and 2.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:506:y:2018:i:c:p:520-531
    DOI: 10.1016/j.physa.2018.04.092
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    References listed on IDEAS

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    6. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 371-383.
    7. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
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