Lump-type kink wave phenomena of the space-time fractional phi-four equation

This article examines the space-time fractional phi-four (PF) model which is an improvement of the Klein-Fock-Gordon (KFG) model that is relevant in quantum mechanics, transmission of ultra-short pulses in optical fibers, de Broglie wave duality, and compound particles in spinless relativistic systems. New solitary wave solutions of the fractional phi-four equation were found with the help of the Riccati-Bernoulli sub-ODE method together with the Bäcklund transformation. The conformable fractional derivative played the role of improving the modeling of the complex dynamical systems. The obtained solutions, which were illustrated by giving 2D, 3D MATLAB plots and contour illustrations, were s eful in nuclear, particle physics and fluid mechanics. Thus, the current work demonstrates the applicability of the proposed approach in handling the fractional order deviations and contributes to the investigation of the dynamic behavior of the PF model.