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

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

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)139-145
Number of pages7
JournalChaos, Solitons and Fractals
Volume125
DOIs
Publication statusPublished - Aug 2019
Externally publishedYes

Keywords

  • Existence
  • Fractional model
  • KdVB-equation
  • Mittag–Leffler Kernel
  • Uniquenes
  • Wave dynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics

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