| Summary: | In the field of mathematical physics, the Riccati sub-equation method is an important tool for locating the analytical solutions of nonlinear space–time fractional equations. In this study, we provide the Riccati sub-equation method for solving the space–time fractional equation by means of the Ablowitz–Kaup–Newell–Segur (AKNS) equation and the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony (GZK-BBM) equation, which explain the effect of flood waves and plasma physics, respectively, and reach new analytical solutions, including parameters. Each equation yields fifteen different solutions, which are in the form of generalized hyperbolic functions, generalized triangular functions, and rational functions. The effect of the arising graphs of both equations is in the form of kink waves and periodic waves, which are presented in 2D and 3D graphs.
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