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Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow

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Abstract

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, 221008, China

    Xiao-Jun Yang

  2. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida 431, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

  3. Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 8 Kliment Ohridsky, blvd, 1756, Sofia, Bulgaria

    Jordan Hristov

Authors
  1. Xiao-Jun Yang
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  2. J. A. Tenreiro Machado
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  3. Jordan Hristov
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Correspondence to Xiao-Jun Yang.

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Yang, XJ., Machado, J.A.T. & Hristov, J. Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow. Nonlinear Dyn 84, 3–7 (2016). https://doi.org/10.1007/s11071-015-2085-2

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  • DOI: https://doi.org/10.1007/s11071-015-2085-2

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