The primary goal of this research is to look into the dynamical behavior of a fractional and fractal-fractional (FF) order laser chaotic model. The model is first considered with Caputo’s fractional derivative. An iterative technique based on the Laplace transform and its inverse aspect is used to achieve a particular solution for the fractional model. The existence of a unique solution is examined for the fractional laser chaotic model. Next, the laser chaotic model is addressed with a FF approach in the Caputo sense. The approximate results are achieved for the proposed fractional and FF models by using the Atangana–Seda numerical methods. The dynamical structures are plotted at various values of fractional and FF parameters.

本研究的主要目标是研究分数和分形分数 (FF) 阶激光混沌模型的动力学行为。该模型首先考虑 Caputo 的分数导数。基于拉普拉斯变换及其逆方面的迭代技术用于实现分数模型的特定解决方案。检查分数激光混沌模型是否存在唯一解。接下来，使用 Caputo 意义上的 FF 方法处理激光混沌模型。通过使用 Atangana-Seda 数值方法，为所提出的分数和 FF 模型获得了近似结果。动态结构以分数和 FF 参数的不同值绘制。