New Wave Solutions of Time-Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation as A Model of Water Waves

Atilgan E., Senol M., Kurt A., Tasbozan O.

CHINA OCEAN ENGINEERING, vol.33, pp.477-483, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33
  • Publication Date: 2019
  • Doi Number: 10.1007/s13344-019-0045-1
  • Journal Name: CHINA OCEAN ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.477-483
  • Keywords: time fractional coupled Boussinesq-Whitham-Broer-Kaup equation, conformable fractional derivative, auxiliary equation method, OPTICAL SOLITONS, POWER-LAW, SYSTEM, NONLINEARITY
  • Eskisehir Osmangazi University Affiliated: No

Abstract

The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq-Whitham-Broer-Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann-Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann-Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.