Abstract
In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described. Also, the fractional derivatives in the sense of beta-derivative are defined. Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation beta-derivative.,ese equations are analyzed utilizing an integration scheme, namely, the rational exp(-Omega(eta))-expansion method. Different kinds of traveling wave solutions such as solitary, topological, dark soliton, periodic, kink, and rational are obtained as a by product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown.,e outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so on.