Existence of periodic, solitary and compacton travelling wave solutions of a $$(3+1)$$-dimensional time-fractional nonlinear evolution equations with applications

Abstract

In this paper, we consider the bifurcation method of dynamical systems for solving time fractional nonlinear evolution equations. We adapt and modify the methodology, incorporating new ideas from the conformable fractional derivative, to investigate exact travelling wave solutions and bifurcations of phase transitions for nonlinear evolution equations. In this study, we show the existence of periodic wave solutions, kink and anti-kink wave solutions, a bright and dark solitary wave solution and parabolic solutions. Moreover, numerical simulations method is applied to show the richer dynamical behavior of the spatial and temporal fractional order of nonlinear evolutions systems and verify the theoretical results.