The nonlinear wave dynamics of the space-time fractional van der Waals equation via three analytical methods

In this paper, we explore the new exact soliton solutions of the truncated M-fractional nonlinear (1 + 1)-dimensional van der Waals equation by applying the exp a function method, extended ( G ' / G )-expansion method, and modified simplest equation method. The concerned equation is a challenging problem in the modeling of molecules and materials. Noncovalent van der Waals or dispersion forces are frequent and have an impact on the structure, dynamics, stability, and function of molecules and materials in biology, chemistry, materials science, and physics. The results obtained are verified and represented by two-dimensional, three-dimensional, and contour graphs. These results are newer than the existing results in the literature due to the use of fractional derivative. The achieved solutions will be of high significance in the interaction of quantum-mechanical fluctuations, granular matter, and other areas of van der Waals equation applications. Therefore, the obtained solutions are valuable for future studies of this model.