Abundant analytical solutions of the fractional nonlinear (2 + 1)-dimensional BLMP equation arising in incompressible fluid

New analytical wave solutions are investigated of the fractional nonlinear [Formula: see text]-dimensional Boiti–Leon–Manna–Pempinelli equation to explain more physical properties of the dynamical behavior of the incompressible fluid. A new fractional definition is used through the modified Khater method to get novel solitary wave solutions of this model. The stability property of the obtained solutions is tested to show the ability of our obtained solutions in using through the physical experiments. The novelty and advantage of the proposed method are illustrated by applying to this model. Some sketches are plotted to show more about the dynamical performance of this model.