New classes of wave solutions for nonlinear conformable space-time PDEs via the Riccati sub-equation approach: analysis of the Bateman-Burgers, Clannish Random Walker's parabolic, and Estevez-Mansfield-Clarkson equations

In this article, we study and introduce travelling wave properties of some nonlinear space-time fractional partial differential equations in applied physics, and the most important is to find analytical solutions for them. We treated in this study the nonlinear space-time fractional Bateman-Burgers equation, the Clannish Random Walker’s Parabolic equation (CRWPE), and Estevez-Mansfield-Clarkson equation (EMCE), which describe traffic flow, shoal waves, and earthquake oscillations, respectively, by combining Riccati sub-equation approach and the conformable derivative. The results obtained consisted of generalized of hyperbolic, triangular, and rational functions. In addition, contour plots, two-and three-dimension are used to describe kinks, a periodic physical wave status. Therefore, as a result, we have contributed a novel and intriguing set of solutions to the suggested nonlinear space-time PDEs with respect to conformable fractional derivatives.