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

作　　者：Emrah ATILGAN Mehmet SENOL Ali KURT Orkun TASBOZAN 

机构地区：[1]Department of Management Informatics Systems, Mustafa Kemal University, Hatay, Turkey [2]Department of Mathematics, Nevsehir Haci Bektas Veli University, Nevsehir, Turkey [3]Department of Mathematics, Pamukkale University, Denizli, Turkey [4]Department of Mathematics, Mustafa Kemal University, Hatay, Turkey

出　　处：《China Ocean Engineering》2019年第4期477-483,共7页中国海洋工程（英文版）

摘　　要：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.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.

关 键 词：time FRACTIONAL COUPLED Boussinesq–Whitham–Broer–Kaup EQUATION conformable FRACTIONAL derivative AUXILIARY EQUATION method 

分 类 号：P[天文地球]