A family of solutions of the time–space fractional longitudinal wave equation

Abstract

Abstract In this article, we have studied a nonlinear time–space fractional longitudinal wave equation in the context of the conformable fractional derivative. Through the soliton ansatz method and a direct integration approach with the symmetry condition, new soliton and solitary wave solutions are derived. Furthermore, the existing conditions of these obtained solutions are also given in this text. These new results add to the existing literature. We believe that they can provide a new window into the understanding of this model.