On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method

In this paper, we mainly study the time-space fractional strain wave equation in microstructured solids. He's variational method, combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation. The main advantage of the variational method is that it can reduce the order of the differential equation, thus simplifying the equation, making the solving process more intuitive and avoiding the tedious solving process. Finally, the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method. The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics. (paper)