The main goal of this paper is to discover some new analytical solutions of a fractional form of the Bogoyavlensky–Konopelchenko equation via two new analytical schemes. This model is considered as a particular case of (2 + 1)–dimensional version of the well–known KdV equation where it describes the interaction between the Riemann wave propagating and the long-wave propagation along the $x,y$–axises. An efficient fractional derivative called Atangana–Baleanu-Riemann derivative is utilized to convert the standard form of the model into a nonlinear fractional PDE with an–integer order. The basic idea in these methods is to use a new variable to transform the form of the equation into a nonlinear equation with ordinary derivatives. The novelty of the present paper is that the new solutions determined by applying these two powerful analytical methods can not be found in previous articles. Several two and three-dimensional figures have been depicted to illustrate the dynamic behavior of the acquired solutions. Another advantage of these two methods is their applicability in solving similar models using this fractional derivative operator.

本文的主要目的是通过两个新的解析方案，发现Bogoyavlensky-Konopelchenko方程的分数形式的一些新解析解。该模型被认为是众所周知的KdV方程（2 +1）维版本的一种特殊情况，其中描述了黎曼波传播与沿波长波传播之间的相互作用。$X，ÿ$–轴。一种有效的分数阶导数称为Atangana–Baleanu-Riemann导数，用于将模型的标准形式转换为具有整数阶的非线性分数PDE。这些方法的基本思想是使用新变量将方程的形式转换为具有常导数的非线性方程。本文的新颖之处在于，通过应用这两种强大的分析方法确定的新解决方案在以前的文章中找不到。已描绘了几个二维和三维图，以说明所获取解决方案的动态行为。这两种方法的另一个优点是它们适用于使用该分数导数算子求解相似模型的情况。