Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the $$\exp \left( { - \phi \left( \varepsilon \right)} \right)$$ exp - ϕ ε -expansion method

Abstract

Nonlinear fractional Boussinesq equations are considered as an important class of fractional differential equations in mathematical physics. In this article, a newly developed method called the $$\exp \left( { - \phi \left( \varepsilon \right)} \right)$$ -expansion method is utilized to study the nonlinear Boussinesq equations with the conformable time-fractional derivative. Different forms of solutions, including the hyperbolic, trigonometric and rational function solutions are formally extracted. The method suggests a useful and efficient technique to look for the exact solutions of a wide range of nonlinear fractional differential equations.