Abstract
The purpose of this article is to construct some novel exact travelling and solitary wave solutions of the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky equation, and two different forms of integration schemes have been utilized in this context. As a result, a variety of bright and dark solitons, kink- and antikink-type solitons, hyperbolic functions, trigonometric functions, elliptic functions, periodic solitary wave solutions and travelling wave solutions are obtained, and the sufficient conditions for the existence of solution are also discussed. Moreover, some of the obtained solutions are illustrated as two- and three-dimensional graphical images by using computational software Mathematica. These types of solutions have a wide range of applications in applied sciences and mathematical physics. The proposed methods are very useful for solving nonlinear partial differential equations arising in physical science and engineering.