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, cilt.33, ss.477-483, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s13344-019-0045-1
  • Dergi Adı: CHINA OCEAN ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.477-483
  • Anahtar Kelimeler: time fractional coupled Boussinesq-Whitham-Broer-Kaup equation, conformable fractional derivative, auxiliary equation method, OPTICAL SOLITONS, POWER-LAW, SYSTEM, NONLINEARITY
  • Eskişehir Osmangazi Üniversitesi Adresli: Hayır

Özet

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.