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

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'/G2)-extension method which works well and reveals exact solutions is used to examine nonlinear Boussinesq equations with conformable time-fractional derivative. This method is a very useful approach and extremely utility 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. © 2022, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.