In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered. These models are
including (space-time fractional order Boussinesq equation; the space-time (2+1)-dimensional breaking soliton equations; spacetime fractional order SRLW equation) which describe the behavior of these equations in the diverse applications. Meanwhile,
the fractional derivatives in the sense of β-derivative are defined. Some fractional PDEs will convert to the considered ordinary
differential equations (ODEs) by the help of transformation β-derivative. These equations are analyzed utilizing an integration
scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions: solitary,
topological, dark soliton, periodic, kink, and rational fall out as a by-product of this scheme. Finally, the existence of the
solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing
finding in the engineering sciences, mathematical physics, and so forh.