Soliton solutions for time fractional ocean engineering models with Beta derivative

Abstract

In this study, the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation (SRLW) and Ostrovsky equation (OE) both arising as a model in ocean engineering. For this aim modified extended tanh-function (mETF) is used. While using this method, chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer order. Owing to the chain rule, there is no further requirement for any normalization or discretization. Beta derivative which involves fractional term is used in considered mathematical models. Obtaining the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.

Keywords

• Symmetric regularized long wave equation
• Beta derivative
• Ostrovsky equation
• Analytical solution
• Soliton solutions
• Periodic wave solution