The nonlinear fractional model, videlicet, the space–time fractional (2+1)-dimensional fractional Bogoyavlenskii equations is an important nonlinear mathematical model to elucidate the hydrodynamic model of shallow water wave, plasma physics, the wave of leading fluid flow etc. This paper is devoted to studying the dynamics of the traveling wave with fractional conformable nonlinear evaluation equations (NLEEs) arising in nonlinear wave mechanics. By utilizing of oncoming exp(- K(ρ))-expansion technique and rational tan(K(ρ))-expansion technique where are the series of novel exact solutions in terms of rational, periodic and hyperbolic functions for the fractional cases are derived. These types of long wave propagation phenomena play a dynamic role to interpret the water waves as well as mathematical physics. It has been demonstrated that our proposed methods are further efficient, general, succinct, power full, straight forward and can be asserted to install the new exact solutions of different kinds of fractional equations in engineering and nonlinear dynamics.
