New Wave Solutions of Time-Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation as A Model of Water Waves
CHINA OCEAN ENGINEERING, cilt.33, ss.477-483, 2019 (SCI-Expanded, Scopus)
- 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.