The Hirota bilinear method is prepared for searching the diverse soliton solutions for the fractional generalized Calogero‐Bogoyavlenskii‐Schiff‐Bogoyavlensky‐Konopelchenko (CBS‐BK) equation. Also, the Hirota bilinear method is used to finding the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and multi‐kink soliton solutions will be investigated. Also, the solitary wave, periodic wave, and cross‐kink wave solutions will be examined for the fractional gCBS‐BK equation. The graphs for various fractional order α are plotted to contain 3D plot, contour plot, density plot, and 2D plot. We construct the exact lump and interaction among other types solutions, by solving the under‐determined nonlinear system of algebraic equations for the associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed. The existence conditions are employed to discuss the available got solutions.

中文翻译：

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分数广义CBS-BK方程的整块，周期波和扭结解之间的相互作用

准备了Hirota双线性方法来搜索分数阶广义Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky-Konopelchenko（CBS-BK）方程的各种孤子解。同样，使用Hirota双线性方法来找到块和与两个条纹孤子解的相互作用。团块，周期波和多结孤子解之间的相互作用将被研究。此外，还将检查分数gCBS-BK方程的孤波，周期波和跨扭波解。各种分数阶α的图绘制以包含3D图，轮廓图，密度图和2D图。通过求解欠定的相关参数代数方程的非线性系统，我们构造了其他类型解决方案之间的精确团块和相互作用。最后，进行了分析和图形仿真，以显示我们解决方案的动力学特性并揭示了相互作用行为。利用存在条件讨论可获得的解。