Analyzing numerous travelling wave behavior to the fractional-order nonlinear Phi-4 and Allen-Cahn equations throughout a novel technique

•Achieve traveling wave solutions, for space-time fractional coupled Boussinesq–Burger and coupled Boussinesq eqn.•Extended tanh-function technique is used for solving the class of NLFPDEs.•Solutions are described through 3D, contour, three dimensional listpoint plots and vector plots.•To study the transmission of shallow-water waves, flow within vertically well-mixed water bodies, and so on. Nonlinear fractional partial differential equations (NLFPDEs) are well suited for describing a broad range of factors in engineering and science, including plasma physics, optical fiber, acoustics, finance, turbulence, mechanical engineering, control theory, nonlinear biological systems, and so on. Through this memorandum, a novel technique is used for solving the class of NLFPDEs. We opted to construct a traveling wave solution to the nonlinear space-time fractional Phi-4 and Allen-Cahn (AC) equations, which are often used as frameworks for a variety of phenomena such as nano fluids, reaction–diffusion model and used to investigate the phase separation process in a variety of components, order–disorder interchange in the bass system and, so on. The subsidiary new generalized (G'/G)-expansion technique for the mentioned equations is used to obtain new precise solutions with the help of conformable derivatives. This strategy is utilized in this article to obtain some new, appealing, and more general outcomes that are simple, versatile, and faster to simulate. Using the proposed technique, some dynamical wave shapes of compaction types, periodic compaction type, single soliton type, kink types, singular kink types, and some other types are accomplished and we used Mathematica to describe the solutions through 3D, contour, 3D list point plot, and vector plots to describe the physical sketch more clearly.