Exact traveling wave solution of Dullin-Gottwald-Holm equation with conformable fractional derivative

The present study focuses on the Dullin-Gottwald-Holm equation, which incorporates a conformable fractional derivative. Employing the two-scale transform and traveling wave transformation, along with the integration of hyperbolic functions and Jacobi elliptic functions, a comprehensive and systematic investigation is conducted. Consequently, the precise traveling wave solutions of this equation have been derived. A thorough discussion is presented on the impacts of various parameters on the properties of the solutions. Furthermore, the approach employed in this paper demonstrates considerable promise in addressing a broader range of non-linear fractional differential equations. It is anticipated that this will pioneer novel concepts and methods in related research areas.