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A behavioral analysis of KdVB equation under the law of Mittag–Leffler function

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  • Doungmo Goufo, Emile F.
  • Tenkam, H.M.
  • Khumalo, M.

Abstract

The literature on fluid dynamics shows that there still exist number of unusual irregularities observed in wave motions described by the Korteweg–de Vries equation, Burgers equation or the combination of both, called Korteweg–de Vries–Burgers (KdVB) equation. In order to widen the studies in the topic and bring more clearness in the wave dynamics, we extend and analyze the KdVB-equation with two levels of perturbation. We combine the model with one of the fractional derivatives with Mittag–Leffler Kernel, namely the Caputo sense derivative with non-singular and non-local kernel (known as ABC-derivative (Atangana–Beleanu–Caputo)). After a brief look at the dynamics of standard integer KdVB-equation, we analyze the combined fractional KdVB-equation by showing its existence and uniqueness results. Numerical simulations using the fundamental theorem of fractional calculus show that the dynamics for the combined model is similar to the integer order dynamics, but highly parameterized and controlled by the order of the fractional derivative with Mittag–Leffler Kernel.

Suggested Citation

  • Doungmo Goufo, Emile F. & Tenkam, H.M. & Khumalo, M., 2019. "A behavioral analysis of KdVB equation under the law of Mittag–Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 139-145.
    • Handle: RePEc:eee:chsofr:v:125:y:2019:i:c:p:139-145
    DOI: 10.1016/j.chaos.2019.05.020
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    Cited by:

    1. Sadeghi, S. & Jafari, H. & Nemati, S., 2020. "Operational matrix for Atangana–Baleanu derivative based on Genocchi polynomials for solving FDEs," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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