The propagation attributes of waves and its modeling maneuvers have a significant role in maritime, coastal engineering, and ocean. In the geographical fields, waves are primary source of environmental process owed to energy conveyance on the floating structure or on the synthetic field. This study aims to investigate the new auxiliary equation method to obtain analytical solutions of the nonlinear Hirota model with fractional order. The fractional model is developed by utilizing Riemann–Liouville, $𝔅$, and the fractional-order Atangana–Baleanu differential operator in Riemann–Liouville sense. The solitonic patterns of the nonlinear fractional Hirota equation successfully surveyed, where the exact solutions are presented by rational, trigonometric, hyperbolic, and exponential functions. The contravene of surveyed results with the substantially recognized result is executed which states the novelty of obtained results. Three dimensional as well as two-dimensional comparison is presented for a couple of Hirota model solutions which are revealed diagrammatically for appropriate parameters by using Mathematica. We strongly believe that this study will help physicists to predict some new conceptions in the field of mathematical physics.

波的传播属性及其建模操作在海洋、海岸工程和海洋中具有重要作用。在地理领域中，由于漂浮结构或合成领域的能量传输，波浪是环境过程的主要来源。本研究旨在研究新的辅助方程法求解分数阶非线性广田模型的解析解。分数模型是利用 Riemann-Liouville 开发的，$𝔅$，以及黎曼-刘维尔意义上的分数阶 Atangana-Baleanu 微分算子。成功调查了非线性分数阶 Hirota 方程的孤子模式，其中精确解由有理函数、三角函数、双曲线函数和指数函数表示。调查结果与实质上认可的结果相抵触，说明所得结果的新颖性。给出了几个 Hirota 模型解决方案的三维和二维比较，这些解决方案通过使用Mathematica以图形方式显示适当的参数。我们坚信这项研究将有助于物理学家预测数学物理领域的一些新概念。