Abstract
In this analysis, we propose a mathematical approach named the extended (ℵ, ℜ) expansion scheme to integrate nonlinear fractional and classical evolution models. We utilize the technique to the time fractional Bogoyavlenskii equation, which signifies the (2 + 1)-dimensional interaction of propagating Riemann waves along a definite axis and a wave normal to it. Additionally, we integrate the model using the new extended (G′/G) expansion scheme. Consequently, we derive exact wave solutions, including singular and multiple periodic soliton solutions, kink waves, anti-kink waves, bell-shaped waves, lump waves, rogue waves, periodic lump waves, and interactions between lump and kink wave profiles. The properties of the fractional parameter on the achieved outcomes are also analyzed. We have created 3D plots, 3D plots with contour lines, and 2D plots of our attained solutions using the computational software, Maple. These systems can also represent various solutions for other fractional models in the domains of nonlinear science and engineering.
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