New analytical solutions of fractional symmetric regularized-long-wave equation

Abstract

In this study, the new extended direct algebraic method (NEDAM) is successfully implemented to acquire new exact wave solution sets for the symmetric regularized-long-wave (SRLW) equation which arises in long water flow models. With the help of the symbolic calculation package Mathematica, the method produced a great number of analytical solutions. We also presented a few graphical illustrations for some surfaces. The fractional derivatives are considered in the conformable sense. All of the solutions were validated by substitution to the equation to ensure the reliability of the method. Obtained results confirm that this is a straightforward, powerful, and effective method to attain exact solutions for nonlinear fractional differential equations. Therefore, the method is a good candidate to take part in the existing literature.