In this paper, we examine a modified auxiliary equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This model is one of the fractional nonlinear partial differential equations. We used conformable derivatives properties to convert nonlinear fractional partial differential equation into the ordinary differential equation with integer order. We obtained many different kinds of solutions such as kink and anti-kink, dark, bright, shock, singular, periodic solitary wave.

In many industrial products stretching surfaces and magnetohydrodynamics are being used. The purpose of this article is to analyze magnetohydrodynamics (MHD) non-Newtonian Maxwell fluid with nanomaterials in a surface which is stretching exponentially. Thermophoretic and Brownian motion effects are incorporated using Buongiorno model. The given partial differential system is converted into nonlinear ordinary differential system by employing adequate self-similarity transformations. Locally series solutions are computed using BVPh 2.0 for wide range of governing parameters. It is observed that the flow is expedite for higher Deborah and Hartman numbers. The impact of thermophoresis parameter on the temperature profile is minimal. Mathematically, this study describes the reliability of BVPh 2.0 and physically we may conclude the study of stretching surfaces for non-Newtonian Maxwell fluid in the presence of nanoparticles can be used to obtain desired qualities.