The main purpose of this research is to inquire the new solitary wave solution of the coupled time-fractional models to validate the influence and proficiency of the planned variational iteration method (VIM) using conformable derivative definition. Applications to four demanding nonlinear problems like Hirota-Satsuma coupled KdV equations, modified Boussinesq (MB) equation, approximate long wave (ALW) equation and Drinfeld-Sokolov-Wilson (DSW) equation demonstrate the efficiency and the robustness of the method. An analysis of the consequences with effects of relevant parameters and comparison with the exact solution presented with the help of graphs tables and gives the further understanding of numerical results by others. The convergence of the method is illustrated numerical and their physical significance is discussed

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In soliton theory, nonlinear mathematical models and their solutions have great importance due to their geometrical behavior. The major focus of this article is to discover solutions of the traveling wave for the equation of foam drainage and NLEEs of 4 th order. The (G'/G)-expansion approach is used on these nonlinear differential equations. With the proper utilization of complex transform these nonlinear PDEs are converted into an ODE. It is noticed that (G'/G)-expansion technique is a sophisticated and accessible tool in engineering, optics, and mathematical physics to find solutions for NLEEs. The method proposed is very efficient and responsible.

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