On exact solutions of some important nonlinear conformable time-fractional differential equations

TL;DR

This paper applies the (G'G^2)-extension method to find exact solutions of nonlinear conformable time-fractional Boussinesq equations, revealing hyperbolic, trigonometric, and rational solutions, and demonstrating its effectiveness over other methods.

Contribution

It introduces the (G'G^2)-extension method for solving nonlinear conformable time-fractional equations, providing explicit solutions and showing its advantages over existing analytical techniques.

Findings

Obtained hyperbolic, trigonometric, and rational solutions.

Demonstrated the method's effectiveness compared to other approaches.

Applicable to other nonlinear fractional models.

Abstract

The nonlinear fractional Boussinesq equations are known as the fractional differential equation class that has an important place in mathematical physics. In this study, a method called (G'G^2)-extension method which works well and reveals exact solutions is used to examine nonlinear Boussinesq equations with conformable time-fractional derivatives. This method is a very useful approach and extremely useful compared to other analytical methods. With the proposed method, there are three unique types of solutions such as hyperbolic, trigonometric and rational solutions. This approach can similarly be applied to other nonlinear fractional models.