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

ATILGAN E., Senol M., Kurt A., TAŞBOZAN O.

China Ocean Engineering, cilt.33, sa.4, ss.477-483, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 4
  • 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: auxiliary equation method, conformable fractional derivative, time fractional coupled Boussinesq–Whitham–Broer–Kaup equation
  • Hatay Mustafa Kemal Üniversitesi Adresli: Evet

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.